The title for the Gospel of Matthew, "According to Matthew". Does anyone know who and when the earliest reference was made that St. Matthew wrote his own Gospel?
Eusebius, writing in the fourth century, referred to Papias as having written about Matthew as an author of what may be the Gospel that now bears the name of Matthew:
Church History 3:39:16: But concerning Matthew he writes as follows: “So then Matthew wrote the oracles in the Hebrew language, and every one interpreted them as he was able.
Assuming Eusebius' sources were good, Papias would therefore have made this attribution around 120 CE.
Although tradition says that Papias was indeed attributing the Gospel to Matthew, there is some uncertainty as to the reliability of Papias and even of Eusebius. Bart D. Ehrman says, in Forged, page 226, there is nothing to indicate that when Papias referred to Matthew and Mark, he was referring to the gospels that were later called Matthew and Mark. Others point out that Papias refers to the writing of Matthew as sayings, or 'oracles', but what we now know as Matthew's Gospel is not a list of sayings. So, although Papias, in around 120 CE, is likely to have made the earliest attribution to Matthew of the Gospel that now bears his name, this is not entirely certain. We know that by the latter half of the second century, the attribution to Matthew was well established.