Tensions between the historical Paul and Peter (Cephas in Aramaic) are attested early on, as Paul's retelling of an incident at Antioch suggests. There, so Paul says in his letter to followers of Christ in Galatia, Paul "opposed [Cephas] to his face" because Cephas had withdrawn from eating with uncircumcized Gentiles after "certain people" came from James, the leader of the church at Jerusalem (see Galatians 2:11-14 [NRSV]). Peter's concern evidently centred on properly following the Jewish food laws. F.C. Baur and the Tübingen school made this opposition between Paul and Peter the key to interpreting all of early Christianity, as I have mentioned in a previous post in this series (no. 2). Although this reduction of early Christianity to these two camps (Pauline Gentile Christianity vs. Petrine Jewish Christianity) is oversimplified, there are times when the figures of Peter and Paul, as understood by later interpreters, continued to be at odds with one another.
The novelistic stories about Clement of Rome and his conversion under Peter's direction, which are known as the Pseudo-Clementines, illustrate continuing battles that existed between some who claimed Peter as their founder (Jewish Christians, who can be associated with "Ebionites") and others who considered Paul as most central (Gentile Christians who no longer followed the Jewish law). Previously I have discussed the notion of "false passages" in scripture that comes up in this writing. (It is important to mention that the form in which we now have this Christian novel comes from two alternate retellings of the fourth century known as the Recognitions and the Homilies, which likely reflect an earlier edition of the mid-200s, the so-called "basic document"; see the introductory material in Strecker's translation in Schneelmelcher). The full text of both the Recognitions and the Homilies is available online here.
The author of this novel presents a Peter who emphasizes the need to follow the Jewish law and opposes another figure, his "enemy", who does not (often called Simon the Samaritan or Magician [Magus] but sometimes clearly a cipher for Paul) . In the supposed letter from Peter to James that prefaces the novel, Peter complains that some "from among the Gentiles have rejected my lawful preaching and have preferred a lawless and absurd doctrine of the man who is my enemy. And indeed some have attempted, while I am still alive, to distort my words by interpretations of many sorts, as if I taught the dissolution of the law and, although I was of this opinion, did not express it openly. But that may God forbid! For to do such a thing means to act contrary to the law of God which was made known by Moses and was confirmed by our Lord in its everlasting continuance. For he said: 'The heaven and earth will pass away, but one jot or one tittle shall not pass away from the law '"(Epistula Petri 2:2- 5; trans. by Strecker in Schneemelcher; cf. Matthew 24:35).
Clearly, the Pseudo-Clementine literature attests to a form of Jewish Christianity (sometimes labelled "Ebionite") which continued to practice the Jewish law and to oppose those it considered to be neglecting the law, namely the heirs of Paul and a Gentile brand of Christianity (including Marcion). There also seems to be a reference here to some portrayals of Peter which tried to lessen any conflict with Paul by presenting Peter as though he did not require obedience to the law (see, for example, the Acts of the Apostles' portrayal of a Paul and Peter, whose speeches on inclusion of Gentiles sound very much alike). Later in the Pseudo-Clementine stories of Clement's journey to Judea and conversion there is a disputation which takes place between Peter and one Simon Magus (the Samaritan), Peter's "enemy", which again sometimes clearly serves as a cipher for a "lawless" Paul who had a supposed vision of Jesus (esp. H II 16-17; H XVII 13-19). Paul's relaxing (for Gentiles) of certain aspects of the Jewish law (including circumcision and food laws) in order to include Gentiles in the Jesus movement was the focus of controversy in Paul's lifetime (read Galatians) and, long after, continued to arouse the response or anger of some Jewish Christians who felt themselves in continuity with Jewish figures such as Peter.
UPDATE (Oct 21): A relevant article on the fourth-century Recognitions version of the Pseudo-Clementines has appeared. Nicole Kelley argues, among other things, that the author of the Recognitions attempts to establish the authority and ultimate knowledge of Peter (via the True Prophet, Jesus) over against other claims to knowledge (especially astrology's claims of true knowledge with respect to "fate", but also claims of knowledge among competing forms of Christianity). And she places this assertion of Peter's access to true knowledge within the context of religious rivalries in fourth century Syria (among Jewish Christians and followers of Marcion, Bardaisan, and others). The romance (story of Clement's family) in particular functions in this manner: The old astrologer's claim that "fate" determined the dissolution of Clement's family is countered successfully by Peter's knowledge that God's providence, not fate, was at work. And the reunion of Clement's family proves Peter (and the source of his knowledge, the True Prophet) right. See Nicole Kelley, "Problems of Knowledge and Authority in the Pseudo-Clementine Romance of Recognitions," Journal of Early Christian Studies> 13 (2005) 315-348 (online institutional subscription required).