Mark (John Mark) wrote the Gospel of Mark but Papias believed that Peter is the original source for this material since Mark spent considerable time with Peter, particularly in Rome, and likely wrote down Peter’s eyewitness account of his experiences with Jesus while Peter was imprisoned in Rome. Papias was Bishop of Hierapolis which is near Laodicea and Colossæ, Papais was an early Apostolic Father and is called by St. Irenæus which is a know hearer of John, and companion of Polycarp. Polycarp is a direct disciple of John, the disciple whom Jesus loved who wrote the Gospel of John.
Papias had reason to believe that Mark was the author of the second gospel but was actually recording what Peter told him so we could actually call it the Gospel of Peter. Papias was said to be quoting the Apostle John. Early church writers seem convinced that Peter is the true source of the Gospel of Mark, since Mark was his aide and interpreter, providing strong external evidence for Mark being the author, and Peter being the oral source including Mark‘s hearing of Peter‘s preaching.
The early church is primarily silent in arguments against Mark’s writing this by Peter’s eyewitness accounts and there was confirmation of Mark‘s authorship of this gospel by Justin Martyr in A.D. 160. Peter also mentions Mark as being with him in Rome while Peter was imprisoned in Rome.
Internal evidence points to Peter being the featured disciple and its being written from Peter’s view because of the writing style and genre are very much like Peter’s books near the end of the New Testament. This evidence of Peter being the source of the Gospel of Mark is his apparent perspective giving vivid detail that seems to come from an eyewitness account of which Mark was not. The clarity and detail is that of one actually being there with Jesus, giving such finite details that only Peter could describe, and the fact that Mark was not present with Jesus during His earthly ministry. Mark’s lack of a chronological order relates more to Peter’s preaching in Acts and reflected in First and Second Peter. Also, this gospel has Peter being, next to Jesus, as the main character and written from a perspective that only Peter could know.
Also, Mark used the Roman system of deriving time for his Roman readers in money and in time (Mark 13:33). Mark is the only one to have recorded Pilates questioning of the Centurion. This confirms the eyewitness report of a Roman military officer. And Mark’s Greek Style contains Semitisms that a Jerusalem Christian would better understand. And Mark was the only one to fully quote Jesus’ cleansing of the Temple from Isaiah 56:7 which included the words “for all nations” indicating to the Roman Christians that God saves Gentiles and Jews alike and seeks both groups worship of Him.
I think it matters less who wrote it because ultimately the Holy Spirit inspired all the men of the Old and New Testament and the intentionality of the Gospel of Mark is like that of all scripture as being “God-breathed”. It is not about the author that is of import, but about the Messiah. The historicity of this Gospel is empirical in nature by the mention of several eyewitnesses and the vivid description and detail with which it is written makes it clear that whoever wrote it. Its authenticity is not affected nor is the effect that it has had and continues to have upon its readers, particularly with the aide of the Holy Spirit which is the bringer of the truthfulness of the scriptures as God-breathed.