Here is my reply, taken from the article written by Lon Martin Titled "Constantine Wrote Matthew 28:19"
Allow me to make this perfectly clear that I do not believe that Constantine wrote matt. 28:19, but however he did oversee and listen to the many arguments presented by some 120 Bishops assembled from throughout the Empire. Utimately endorsing the Nicean Creed, he Constantine help to establish the accepted doctrine of the then Catholic Church.
According to Conybeare:
Eusebius cites this text (Matt. 28:19) again and again in works written between 300 and 336, namely in his long commentaries on the Psalms, on Isaiah, his Demonstratio Evangelica, his Theophany ...in his famous history of the Church, and in his panegyric of the emperor Constantine. I have, after a moderate search in these works of Eusebius, found eighteen citations of Matthew 28:19, and always in the following form: ‘Go ye and make disciples of all the nations in My name, teaching them to observe all things, whatsoever I commanded you.’
Ploughman’s research uncovered all of these quotations except for one, which is in a catena published by Mai in a German magazine, the Zeitschrift fur die neutestamentliche Wissenschaft, edited by Dr. Erwin Preuschen in Darmstadt in 1901. Eusebius was not content merely to cite the verse in this form, but he more than once commented on it in such a way as to show how much he confirmed the wording “in my name”. Thus, in his Demonstratio Evangelica he wrote the following:
For he did not enjoin them “to make disciples of all the nations” simply and without qualification, but with the essential addition “in his name”. For so great was the virtue attaching to his appellation that the Apostle says, "God bestowed on him the name above every name, that in the name of Jesus every knee shall bow of things in heaven and on earth and under the earth." It was right therefore that he should emphasize the virtue of the power residing in his name but hidden from the many, and therefore say to his Apostles, "Go ye, and make disciples of all the nations in my name.’ (col. 240, p. 136)
Conybeare proceeded, in Hibbert Journal, 1902: It is evident that this was the text found by Eusebius in the very ancient codices collected fifty to a hundred and fifty years before his birth by his great predecessors. Of any other form of text he had never heard and knew nothing until he had visited Constantinople and attended the Council of Nice. Then in two controversial works written in his extreme old age, and entitled, the one ‘Against Marcellus of Ancyra,’ and the other ‘About the Theology of the Church,’ he used the common reading. One other writing of his also contains it, namely a letter written after the Council of Nice was over, to his seer of Caesurae.
Hmm, I kind of expected this and have had ample time to formulate a response. First it must be stated that the ancient practice for quotation is not the same as our own. The ancients would often reword a quote to make a point and not quote directly. Now onto other Fathers, most earlier than Eusibius providing the same quotation but in the commonly known Trinitarian form.
Tertullian, c. 200 AD writes in On Baptism, Chapter XIII: "For the law of baptizing has been imposed, and the formula prescribed: "Go," He saith, "teach the nations, baptizing them into the name of the Father, and of the Son, and of the Holy Spirit." and in Against Praxeas, chapter 2 says, "After His resurrection ..He commands them to baptize into the Father and the Son and the Holy Ghost".
Hippolytus (170-236 AD) says in Fragments: Part II.-Dogmatical and Historical.--Against the Heresy of One Noetus, "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 Ghost."
Cyprian (200-258AD) in The Seventh Council of Carthage Under Cyprian says, And again, after His resurrection, sending His apostles, He gave them charge, saying, "All power is given unto me, in heaven and in earth. Go and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost."
Gregory Thaumaturgus (205-265 AD) in A Sectional Confession of Faith, XIII says, "....the Lord sends forth His disciples to baptize in the name of the Father, and of the Son, and of the Holy Spirit?"
Similarly Irenaeus says:
"Wherefore also the Lord, when He sent forth the apostles to make disciples of all nations, commanded them to “baptize in the name of the Father, and of the Son, and of the Holy Ghost,” (Epistle to the Philippians, Chapter II, circa 100-202 AD).
Then of course there is the very early Didache which I provided before, and there is also the fact that every single copy we have of Matthew has Matthew 28:19 in the Trinitarian form we all are familiar with.