The following is a brief selection of the Ante-Nicene (before Nicaea) testimony to this fundamental doctrine of the Christian faith, thus demonstrating that the doctrine of the Trinity is not a later invention of the Church at the Council of Nicaea (A.D. 325), as is frequently asserted by various internet apologists. While the formal articulation of the doctrine of the Trinity was certainly a later development as a result of responding to heretical teachings, what these quotations reveal is that the earliest disciples of Christ referred to Christ as God, recognized Him as being both God and man via the incarnation, and likewise asserted the Deity and personhood of the Holy Spirit. The distinction between the Persons of the Godhead is also maintained.
Ignatius: (Wrote in the early 2nd Century)
“There is only one physician, who is both flesh and spirit, born and unborn, God in man, true life in death, both from Mary and from God, first subject to suffering and then beyond it, Jesus Christ our Lord.” (Epistle to the Ephesians, vii.)
“…because you are stones of a temple, prepared beforehand for the building of God the Father, hoisted up to the heights by the crane of Jesus Christ, which is the cross, using as a rope the Holy Spirit….” (Epistle to the Ephesians, ix.)
“For our God, Jesus the Christ, was conceived by Mary according to God’s plan, both from the seed of David and of the Holy Spirit.” (Epistle to the Ephesians, xviii.)
“…when God appeared in human form to bring the newness of eternal life.” (Epistle to the Ephesians, xix.)
“I glorify Jesus Christ, the God who made you so wise,…he is truly of the family of David with respect to human descent, Son of God with respect to the divine will and power….” (Epistle to the Smyrnaeans, i.)
“…in accordance with faith in and love for Jesus Christ our God…. heartiest greetings blamelessly in Jesus Christ our God.” (Epistle to the Romans, Salutation.)
Author of the Epistle of Barnabas: (Written in the late 1st Century or early 2nd Century)
“And furthermore, my brothers and sisters, if the Lord submitted to suffer for our souls, even though he is Lord of the whole world, to whom God said at the foundation of the world, ‘Let us make humankind according to our image and likeness,’ how is it, then, that he submitted to suffer at the hand of humans? Learn!” (Epistle of Barnabas, v.)
“…the Spirit says to the heart of Moses that he should make a symbol of the cross and of the one who was destined to suffer because, he is saying, unless they place their hope in him, war shall be waged against them forever.” (Epistle of Barnabas, xii.)
Polycarp: (Wrote in the early 2nd Century)
“…and to all those under heaven who will yet believe in our Lord and God Jesus Christ and in his Father who raised him from the dead.” (Epistle to the Philippians, xii.)
Hippolytus: (Wrote during the late 2nd Century to early 3rd Century)
“These things then, brethren, are declared by the Scriptures. And the blessed John, in the testimony of his Gospel, gives us an account of this economy (disposition) and acknowledges this Word as God, when he says, “In the beginning was the Word, and the Word was with God, and the Word was God.” If, then, the Word was with God, and was also God, what follows? Would one say that he speaks of two Gods? I shall not indeed speak of two Gods, but of one; of two Persons however, and of a third economy (disposition), viz., the grace of the Holy Spirit. For the Father indeed is One, but there are two Persons, because there is also the Son; and then there is the third, the Holy Spirit. The Father decrees, the Word executes, and the Son is manifested, through whom the Father is believed on. The economy of harmony is led back to one God; for God is One. It is the Father who commands, and the Son who obeys, and the Holy Spirit who gives understanding: the Father who is above all, and the Son who is through all, and the Holy Spirit who is in all. And we cannot otherwise think of one God, but by believing in truth in Father and Son and Holy Spirit. For the Jews glorified the Father, but gave Him not thanks, for they did not recognize the Son. The disciples recognized the Son, but not in the Holy Spirit; wherefore they also denied Him. The Father’s Word, therefore, knowing the economy (disposition) and the will of the Father, to wit, that the Father seeks to be worshipped in none other way than this, gave this charge to the disciples after He rose from the dead: “Go ye and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Spirit.” (Mtt. 28:19) And by this He showed, that whosoever omitted any one of these, failed in glorifying God perfectly. For it is through this Trinity that the Father is glorified. For the Father willed, the Son did, the Spirit manifested. The whole Scriptures, then, proclaim this truth.” (Against the Heresy of Noetus, xiv.)
“Let us believe then, dear brethren, according to the tradition of the apostles, that God the Word came down from heaven, (and entered) into the holy Virgin Mary, in order that, taking the flesh from her, and assuming also a human, by which I mean a rational soul, and becoming thus all that man is with the exception of sin, He might save fallen man, and confer immortality on men who believe on His name.” (Against the Heresy of Noetus, xvii.)
Now that we have seen these Ante-Nicene articulations of Trinitarian theology, I turn your attention now to the more formalized Nicene Creed, finalized in AD 381:
“We believe in one God, the Father, the Almighty, maker of heaven and earth, of all that is, seen and unseen.
We believe in one Lord, Jesus Christ, the only Son of God, eternally begotten of the Father, God from God, Light from Light, true God from true God, begotten, not made, of one Being with the Father. Through him all things were made. For us and for our salvation he came down from heaven: by the power of the Holy Spirit he became incarnate from the Virgin Mary, and was made man. For our sake he was crucified under Pontius Pilate; he suffered death and was buried. On the third day he rose again in accordance with the Scriptures; he ascended into heaven and is seated at the right hand of the Father. He will come again in glory to judge the living and the dead, and his kingdom will have no end.
We believe in the Holy Spirit, the Lord, the giver of life, who proceeds from the Father and the Son. With the Father and the Son he is worshiped and glorified. He has spoken through the Prophets. We believe in one holy catholic [i.e. universal and historic] and apostolic Church. We acknowledge one baptism for the forgiveness of sins. We look for the resurrection of the dead, and the life of the world to come. Amen.”
 All quotations, except those of Hippolytus, are from The Apostolic Fathers: Greek Texts and English Translations, 3rd Edition, by Michael W. Holmes. The Hippolytus quotations are from Ante-Nicene Fathers, vol. 5.