I Clement, is the earliest known example of extra Biblical Christian writing. It dates to A.D. 95, and according to tradition is the work of the Biship of Rome, Clement, to the Church at Corinth. The issue was rebellion in the ranks of Presbyters. Be that as it may, the author does mention the Apostle Peter and Paul as having been with them in Rome during his own time.
Let us come to the Heroes nearest our own times. Let us take the noble examples of our own generation; by reason of rivalry the greatest and most righteous pillars [of the church] were persecuted and battled to the death. Let us set before our eyes the noble Apostles; Peter who...frequently endured suffering and thus wen to the glorious place which he merited...Paul showed how to win the prize for patient endurance.... [1
This not only documents the connection to Paul, but also to Peter. He speaks of them as part of "our own generation" indicating that this was common knowledge to all of them, that he himself was witness to the presence of these men in Rome. Writing in 95, the events described (64 AD) would have been within living memory of the older members of the congregation. While it is true that this is not direct evidence for Jesus existence, it is evidence that Peter was a real historical person. Since Peter was involved in the center of the action, it is absurd to claim that those events recorded in the Gospels did not take place. We can be certain that they at least had their referent in actual historical events. It is also hard to see how Peter would give his life to a lie, if he made it up or participated in a hoax, never gain from it, and eventually die for that lie. Of course we have already argued that Paul had access to eye witnesses of Jesus' life. So Paul is a reasonble link in the chain. He connects us to the testimony of those who knew Jesus.

Clement souces

[1] The First Epistle of Clement (5:2-5) in Richardson and Fairweather, et al. Early Christian Fathers, New York: MacMillian, 1970,45-46. a foot note of the editor adds that this is good evidence for Peter's martyrdom in Rome (fn Ibid.).