The claim is often made by anti-Trinitarians that the doctrine of the Trinity was not held by the Church Fathers prior to the 4th century, at which time it was formulated and made part of Church dogma by the Council of Nicaea which convened in 325AD.
However, as I hope to demonstrate in this blog, the Church Fathers understood the Godhead as being Triune from the very beginning. It is true that the language they used to express the Trinity was at first limited to general nonspecific affirmations. However, as their beliefs began to come under attack, first by the Gnostics and Modalists, and then later in the 3rd century by the Arians who denied the full deity of Christ and the person of the Holy Spirit, their language of necessity became more precise and specific. The following citations of the Fathers are just a few of hundreds which make it abundantly clear that the Church Fathers believed in the Trinity from the time of the Apostles.
Ignatius (30 – 107AD)
“Since, also, there is but one unbegotten Being, God, even the Father; and one only-begotten Son, God, the Word and man; and one Comforter, the Spirit of truth.” 
While this statement is simply a general affirmation, emphasizing that there are only three who are God, in opposition to the Gnostics who believed that we are all gods, he does nevertheless clearly mention three distinct persons who are God. At the same time, he emphasizes throughout his epistle that there is only one God, so he is clearly not teaching Tritheism.
Justin Martyr (100 – 165AD)
“Therefore neither Abraham, nor Isaac, nor Jacob, nor any other man, saw the Father and ineffable Lord of all, and also of Christ, but saw Him who was according to His will His Son, being God, and the Angel because He ministered to His will; whom also it pleased Him to be born man by the Virgin; who also was fire when He conversed with Moses from the bush. Since, unless we thus comprehend the Scriptures, it must follow that the Father and Lord of all had not been in heaven when what Moses wrote took place: ‘And the Lord rained upon Sodom fire and brimstone from the Lord out of heaven’… and again, when He says: ‘The Lord says to my Lord, Sit at My right hand, till I make Thine enemies Thy footstool.’” 
In the context of this quote, Justin is establishing that Yahweh who was seen in the Theophanies of the Old Testament was not the Father but God the Son; that the Angel of the Lord in the Old Testament was in fact the preincarnate Son of God; that when it says in Genesis 19:24 that Yahweh rained fire upon Sodom from Yahweh, it is referring to the preincarnate Son who was with Abraham and the Father in heaven, just as in Psalms 110:1 says: “Yahweh says to my Adonai, sit at My right hand till I make Your enemies your footstool.” I demonstrate that Jesus is the Yahweh of the Old Testament in my blog, Jesus is the Yahweh of the Old Testament, and also the Angel of Yahweh in my blog, The Christophanies of the Old Testament.
“For, in the name (sing.) of God, the Father and Lord of the universe, and of our Savior Jesus Christ, and of the Holy Spirit, they then receive the washing with water.” 
Speaking of water baptism, Justin Martyr alludes to the Triune baptismal formula given by Jesus in Matthew 28:19, “baptizing them in the name (sing.) of the Father and of the Son and of the Holy Spirit.” While they are three persons, they are nevertheless one in name since they are one God and not three Gods.
Ignatius of Antioch (died 110AD).
“There is one Physician who is possessed both of flesh and spirit; both made and not made (begotten and unbegotten), God existing in flesh; true life in death; both of Mary and of God; first possible and then impossible,- even Jesus Christ our Lord…” 
Here Ignatius speaks of the Son of God as both begotten of Mary and unbegotten as the eternal Son of God (begotten and unbegotten, gennhtos kai agennhtos), God existing in flesh. This is a clear affirmation of the eternal deity of Christ. While it is another subject in itself, begotten is from γεννάω (gennao) and should not be confused with γένος (genos) which means “kind.” Jesus is referred to as the Father’s “only Son” or “unique one of a kind Son” (μονογενής, monogenes), rather than His “only begotten Son.”  Most modern translations reflect this correction.
“The Church, though dispersed throughout the whole world, even to the ends of the earth, has received from the apostles and their disciples this faith: . . . one God, the Father Almighty, Maker of heaven, and earth, and the sea, and all things that are in them; and in one Christ Jesus, the Son of God, who became incarnate for our salvation; and in the Holy Spirit, who proclaimed through the prophets the dispensations of God, and the advents, and the birth from a virgin, and the passion, and the resurrection from the dead, and the ascension into heaven in the flesh of the beloved Christ Jesus, our Lord, and His manifestation from heaven in the glory of the Father ‘to gather all in one,’ and to raise up anew all flesh of the whole human race, in order that to Christ Jesus, our Lord, and God, and Savior, and King, according to the will of the invisible Father, ‘every knee should bow, of things in heaven, and things in earth, and things under the earth, and that every tongue should confess; to him, and that He should execute just judgment towards all . . . ‘” 
In addition to Irenaeus’ obvious references to the final restoration of all, he says that the Church had received from the Apostles and the disciples of the Apostles the belief in one God the Father, one Jesus Christ and in the Holy Spirit, three distinct persons. Additionally, he says that Christ Jesus is Lord and God. This quote contains an allusion to 1 Corinthians 8:6, which says: “yet for us there is one God, the Father, of whom are all things, and we for Him; and one Lord Jesus Christ, through whom are all things, and through whom we live.”
Some Unitarians have mistaken Paul as saying here that only the Father is God. However, both Jesus and the Holy Spirit are also called God in Scripture, therefore they also make up the one Godhead. It also says that there is one Lord, yet we know that the Father and the Holy Spirit are also called Lord in Scripture. Paul was addressing Gentiles of Corinth who had been raised in a polytheistic society, and we see in the context that his objective was to emphasize that for us there is only one God and one Lord, not many.
Athenagoras, (133 – 190AD)
“Who, then, would not be astonished to hear men who speak of God the Father, and of God the Son, and of the Holy Spirit, and who declare both their power in union and their distinction in order, called atheists?” 
“…they know God and His Logos, what is the oneness of the Son with the Father, what the communion of the Father with the Son, what is the Spirit, what is the unity of these three, the Spirit, the Son, the Father, and their distinction in unity.” 
Here we see in the 2nd century a clear expression of the triunity of the Godhead or the Trinity, Father, Son, and Holy Spirit. As iron sharpens iron, the Fathers became more specific and precise in their use of terms as the Scriptural doctrine of God came under attack from different fronts. At this time the distinction of persons within the Godhead was emphasized in response to the Modalists who denied that the one God exists as three persons, saying that Father, Son and Holy Spirit are merely three forms in which the one God manifests Himself. A modern version of Modalism is the Oneness Pentecostals, or Jesus Only Pentecostals.
The Christians at that time were called Atheists because they did not worship the pagan gods; nor would they acknowledge the emperor as being a god.
Tertullian (155 – 220AD)
“Thus the connection of the Father in the Son, and of the Son in the Paraclete, produces three coherent Persons, who are yet distinct One from Another. These Three are one essence, not one Person, as it is said, I and my Father are One, in respect of unity of substance not singularity of number. For just as the Word of God is not actually He whose Word He is, so also the Spirit (although He is called God) is not actually He whose Spirit He is said to be. Nothing which belongs to something else is actually the very same thing as that to which it belongs. He commands them to baptize into the Father and the Son and the Holy Ghost, not into a unipersonal God.” 
In Tertullian’s treatise, Against Praxeas, he is not opposing Arianism, or the denial of the deity of Christ and the person of the Holy Spirit since that was a non-issue at the time, being that Arius wasn’t even born until after Tertullian’s death. Tertullian was opposing the Modalism of Praxeas, who like Sabellius, taught that God was a unipersonal being, with Father, Son, and Holy Spirit simply being three modes or manifestations of that one divine Person. In his treatise, Tertullian uses the word “Trinity” 15 times and emphasizes the Triune nature of God.
He seeks to demonstrate by various examples the logical absurdities one confronts when reading the Scripture as though God were a solitary being rather than Father, Son and Holy Spirit. He says to Praxeas:
“If you want me to believe him to be both the Father and the Son, show me some other passage where it is declared, “The Lord said to himself, ‘I am my own Son, today have I begotten myself.’ … On your side, however, you must make Him out to be a liar, an impostor, and a tamperer with his word, if, when he was himself a Son to himself, he assigned the part of his Son to be played by another. All the Scriptures attest the clear existence of, and distinction of persons in the Trinity, and indeed furnish us with our Rule of faith. He who speaks, and he of whom he speaks and to whom he speaks, cannot possibly seem to be one and the same.” 
He also answers to the claim that Trinitarians are Tritheists, saying:
“Bear always in mind that this is the rule of faith which I profess; by it I testify that the Father, and the Son, and the Spirit are inseparable from each other, and so will you know in what sense this is said. Now, observe, my assertion is that the Father is one, and the Son one, and the Spirit one, and that They are distinct from Each Other. This statement is taken in a wrong sense by every uneducated as well as every perversely disposed person, as if it predicated a diversity, in such a sense as to imply a separation among the Father, and the Son, and the Spirit.” 
In spite of the fact that we as Trinitarians emphatically affirm that we are Monotheists who believe that the one true God is Triune as to Persons, to this day, we continue to be misrepresented as though we were Tritheists, teaching that the Father, Son and Holy Spirit are three separate Gods.
Origen (185 – 254AD).
“But in our desire to show the divine benefits bestowed upon us by Father, Son, and Holy Spirit, which Trinity is the fountain of all holiness, we have fallen, in what we have said, into a digression, having considered that the subject of the soul… We shall, however, with the permission of God through Jesus Christ and the Holy Spirit, more conveniently consider in the proper place the subject of all rational beings, which are distinguished into three genera and species.” 
In his treatise, de Principiis, alone, Origen uses the word “Trinity” to refer to the Godhead over 20 times. Origen emphasized that the Holy Spirit is a person of the Triune Godhead and not merely the impersonal force or influence of God. He said:
“…the person of the Holy Spirit was of such authority and dignity, that saving baptism was not complete except by the authority of the most excellent Trinity of them all, i.e., by the naming of Father, Son, and Holy Spirit.” 
In response to those who claimed that the Son of God was a created being, Origen said:
“How, then, can it be asserted that there once was a time when He was not the Son? For that is nothing else than to say that there was once a time when He was not the Truth, nor the Wisdom, nor the Life, although in all these He is judged to be the perfect essence of God the Father; for these things cannot be severed from Him, or even be separated from His essence. And although these qualities are said to be many in understanding, yet in their nature and essence they are one, and in them is the fulness of divinity. Now this expression which we employ- ‘that there never was a time when He did not exist’ - is to be understood with an allowance. For these very words ‘when’ or ‘never’ have a meaning that relates to time, whereas the statements made regarding Father, Son, and Holy Spirit are to be understood as transcending all time, all ages, and all eternity. For it is the Trinity alone which exceeds the comprehension not only of temporal but even of eternal intelligence; while other things which are not included in it are to be measured by times and ages.” 
Hippolytus of Rome, (170 – 235AD)
“Who will not say that there is one God? Yet, he will not on that account deny the economy.”
“If then the Word was with God and was also God, what follows? Would one say that I speak of two Gods? I will not indeed speak of two Gods, but of one. I speak of two persons, however, and of a third economy – the grace of the Holy Spirit…the economy of harmony is led back to one God. For God is one. The Father who commands, the Son who obeys and the Spirit who gives understanding.” 
The Greek Fathers used the word οἰκονομία “economy or dispensation” to describe the eternal economic complementary relationship between the persons of the Trinity. While they are one as to their essential nature and attributes, and co-eternal and co-equal, their relationship one with the other is distinct. In that sense, Jesus could say that the Father was greater than He, even though they are both the one and only Almighty God (Rev 1:8, cf. 11:17). The Son is eternally in loving submission to the Father and the Holy Spirit always carries out the will of the Father and the Son.
Cyprian of Carthage (210 – 258AD)
“And again, of the Father, Son, and Holy Spirit it is written: ‘And the three are One.’” 
Here we see Cyprian quoting what is commonly referred to as the Comma of 1John 5:7 which says: “For there are three that bear witness in heaven: the Father, the Word, and the Holy Spirit; and these three are one.” While I am not a King James only advocate, I do feel that there are several good arguments for considering the Comma to have been part of the original text. Cyprian here cites it a hundred years before the oldest Greek manuscript we have of 1John, and he quotes it as though it were a commonly known passage in the Church at that time.
The authenticity of 1John 5:7 wasn’t severely challenged until the 19th century. It is true that there are very few later Greek manuscripts which contain the Comma, apart from the many Latin manuscripts which contain it. However, there is reason to believe that it was removed from the Greek texts of the Eastern Orthodox Church under pressure from the Arians, only being retained in the Latin texts by the Latin Church. The Eastern Orthodox Church was battling against Modalistic Sabellianism at the time and the Comma, being one of the favorite prooftexts of the Sabellians, may have made them more willing to part with it.
It is significant that there is no record of anyone insisting that the Comma be included in Scripture before the council of Nicaea. We only have record of the Arians demanding that Gregory remove it, which implies that it was originally there and removed. For anyone who might want to investigate this subject further, Dr. C. H. Pappas, ThM, presents his arguments for its inclusion in his book In Defense of the Authenticity of 1 John 5:7.
Alexander, Bishop of Alexandria (273 – 326AD)
“Therefore, when the holy prophets, and all, as I have said, who righteously and justly walked in the law of the Lord, together with the entire people, celebrated a typical and shadowy Passover, the Creator and Lord of every visible and invisible creature, the only-begotten Son, and the Word co-eternal with the Father and the Holy Spirit, and of the same substance with them, according to His divine nature, our Lord and God, Jesus Christ.” 
Here again, we see another Ante Nicene Father stating that the Son is co eternal with the Father and the Holy Spirit, sharing in the same essence or substance.
All of these quotes are from prominent Church Fathers long before the council of Nicea in 325AD. It is true that, as errors crept into the Church, it became necessary for Church leaders to convene to counter them with formal Church creeds. However, as we have seen, the Trinity was the prevailing doctrine of the Church from the very time of the Apostles.
 The Epistle of Ignatius to the Philadelphians Chapter IV
 Justin Martyr, Dialogue with Trypho, chapter 127
 Justin Martyr First Apology, chapter 61
 Ignatius, commentary on Ephesians, chapter 7
 Against Heresies, Book 10, chapter 1
 Athenagoras. The Sacred Writings of Athenagoras (p. 10). Jazzybee Verlag. Kindle Edition.
 Athenagoras. The Sacred Writings of Athenagoras (pp. 11-12). Jazzybee Verlag. Kindle Edition.
 Tertullian, Against Praxeas, chapter 25
 Tertullian, Against Praxeas, chapter 11
 Tertullian, Against Praxeas chapter 9
 Origen, De Princiipiis, book 1, chapter 4.2
 Origen, De Princiipiis, book 1, chapter 3.2
 Origen, De Princiipiis, book 4, chapter 28
 St. Cyprian, De Lapsis, The Unity of the Catholic Church, chapter 6
 Epistles on the Arian Heresy and the Deposition of Arius. Chapter 1.7