The Muratorian Fragment is currently the oldest list of New Testament books that we have. It was discovered in the Ambrosian Library in Milan by Ludovico Antonio Muratori. Muratoria published the Muratorian Fragment in 1740.
The fragment was probably copied during the seventh century. It’s dated at AD 170 because it says that the episcopate of Pius I of Rome was recent, and Pius I died in AD 157.
The fragment says explicitly that the Gospel of Luke was written by Luke and that the Gospel of John was written by John. The beginning of the fragment is missing, but it can be assumed that it refers to the Gospel of Mark being written by Mark.
It refers to Luke as being “the third book” and John as being the “fourth of the Gospels,” so it can be assumed that the missing part of the fragment referred to Mark as being the “second” gospel and Matthew as being the “first” gospel.
The Muratorian Fragment is another piece of early evidence we have that the authors of the four Gospels are indeed Matthew, Mark, Luke, and John.
. . . 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