There is debate concerning. whether John wrote the Gospel of John. It can be strongly argued that John is in fact the author.
The earliest description of this Gospel that we have says that the Gospel was written by John. The book was circulated with John in the title.
One argument against John being the author is that the titles are not part of the body of the Gospels, so it is suggested that the Gospels were anonymous. However, even if there is no internal evidence that John is the author of the Gospel, the unanimous early tradition that ascribes this Gospel to John is strong evidence that Luke is indeed its author.
Matthew also issued a written Gospel among the Hebrews in their own dialect, while Peter and Paul were preaching at Rome, and laying the foundations of the Church. After their departure, Mark, the disciple and interpreter of Peter, did also hand down to us in writing what had been preached by Peter. Luke also, the companion of Paul, recorded in a book the Gospel preached by him. Afterwards, John, the disciple of the Lord, who also had leaned upon His breast, did himself publish a Gospel during his residence at Ephesus in Asia.Irernaeus, Against Heresies 3:1:1
Here, Irenaeus says that Mark, who is “the interpreter and follower of Peter,” is the author of “his Gospel narrative.” Irenaeus is another early source that says that Mark is the author of the Gospel of Mark.
. . . at which nevertheless he was present, and so he placed. The third book of the Gospel is that according to Luke. Luke, the well-known physician, after the ascension of Christ, when Paul had taken with him as one zealous for the law, composed it in his own name, according to belief. Yet he himself had not seen the Lord in the flesh; and therefore, as he was able to ascertain events, so indeed he begins to tell the story from the birth of John. The fourth of the Gospels is that of John, of the disciples.The Muratorian Fragment
The Muratorian Canon refers to the Gospel of Luke as being the “third” book and the Gospel of John as being the “fourth of the Gospels.”
The Muratorian Canon is another piece of early evidence that John wrote the Gospel of John.