Two different Christianities existed during the last half of the first century.

      James was the leader of  new band of  liberal Jews.  Josephus refers to James taking over.. The Gospel of St Thomas refers to Jesus naming James as the disciples' leader after his own departure. In the Secret Book of James, James occupies the dominant role sometimes attributed to Peter in canonical writings. Church Fathers were aware that James had taken over the leadership of the apostles, and he was acknowledged to have been the first Bishop of Jerusalem. Furthermore it is clear from the New Testament that James (recognised by the Church as James the Just) enjoyed primacy over the other disciples. For example James alone makes the final decision about the dietary laws (Acts 15:13-20). A passage in Galatians gives James's name before Peter's , indicating relative rank (Galatians 2:9). Another makes it clear that Peter felt himself subject to James (Galatians 2:11-12) 

     From the little that the Bible tells us it is apparent that after Jesus" death the disciples continued to live communally. They visited the Temple together every day, gave generously, and were generally well respected (Acts 2:44-7). With the exception of Peter, there is no reason to suppose that any of them left the vicinity of Jerusalem. Nor is there any reason to suppose that they abandoned their Jewish faith*. Had this Jewish line survived there is little doubt that it would have had the strongest claim to represent Jesus" intentions. James was executed at the instigation of the Sadducees, in circumstances similar to those surrounding the death of his brother Jesus*. James was succeeded by another close relation, a cousin called Simeon (or Symeon)*, though this succession seems to have caused dissent and schism*.  )

      Like James and Simeon, some later leaders, or bishops of the circumcision as they were known, were also related to Jesus, suggesting some sort of dynastic succession. Their followers may have precipitated the First Jewish Revolt of AD 66, and certainly suffered from the Roman reaction to it. This faction was virtually wiped out during the Second Jewish Revolt of AD 132. When the Emperor Hadrian banished all Jews from Jerusalem in AD 135 he put an end to this line of "bishops of the circumcision", a string of Jewish bishops of Jerusalem. The Church historian Eusebius listed the whole line from the first, "James the Lord's brother", to the fifteenth and last*.

     After AD 135 only gentiles were permitted to enter the city of Jerusalem, and a new bishop was put in charge of those among them who espoused Christianity*. Presumably he was a gentile of the Pauline line who brought a new orthodoxy. The bishops of the circumcision had lost their throne, but the line of Jewish Christians continued in exile. A sect of Jewish Christians, known as Ebionites, survived for two or three centuries. They retained the Jewish Sabbath, Jewish Law, and other characteristically Jewish practices. Some rejected the doctrine of the Virgin Birth, others rejected the letters of Paul, regarding him as a renegade from the Jewish Law. Some believed that Jesus had supernatural virtue and power, but all denied that he was the son of God in the sense now usually accepted by mainstream Christianity*.

     They became isolated from the Pauline branch of the Church and, from the second century, were regarded by them as heretics*. The Ebionites disappear from history still repudiating Paul as an apostate. Conveniently for rival factions all but a few records concerning Jewish Christianity are lost to us. The New Testament contains only one work that might be thought to reflect their views, the general letter of James. Luther called it "A right strawry epistle", though it is possibly the oldest book of the New Testament. Certainly it expresses views on the importance of faith that contrast sharply with those of Paul.

     Paul starting a new form of Christianity, because Jesus didn't originally claim to be God started after the scientific revolution, or approximately 1700 years after the fact. Because of this, any texts that wasn't directly influenced by Paul is now seen as “non-Pauline.”

The fact of the matter is that Paul himself even taught a unity of belief, saying that the one preaching the gospel to them didn't matter at all. He specifically uses “Cephas” (Peter) as an example in 1 Corinthians 1:12, one of the “Jewish Christians.” Galatians 1 details a fair bit about Paul ensuring that the Gospel stays intact, and that the only ones who instructed him before he started preaching were Peter and James, the two leaders of the “Jewish Christians”.

Now, if by non-Pauline Christians you mean Christians who rejected the Gospel of the apostles in favor of something else that called itself Christian, we can't exactly call that Christian… But that aside, not really. The “gnostic gospels” are a few examples, but some of those were forgeries of the 20th century (like the recent fragment about Mary Magdalene), so it does require care when looking. We have accounts of what they believed, because the first Christians were actively working against them. The best example would probably be some of St. Irenaeus’s writing.