Mark was known as the translator for Peter, so that's the closest you can get to the Petrine tradition for something written in Greek.

The point is that all of the gospels circulated anonymously. Mark may have been written by Mark, but the attribution comes after the real Mark would have been dead. In fact, Mark is the only one of the gospels where the attribution might come early, if Eusebius is correct in his attribution. Matthew doesn't appear at the top of "his" gospel until the Third Century (which means that the Thomas attribution for the Gospel of Thomas predates Matthew's attribution), and Luke remains anonymous to Papias, Justin and Marcion, and only starting with Irenaeus in the late Second Century is there any attribution of a gospel to him (Adv. Haer. 3.1.2). The first time the gospel (together with Acts) is attributed to him at the top of the copy is in the late Second Century.