Marcionism is the main heresy (read: deviation from mainline) that promotes the supremacy of Paul's writings. It's similar to Gnosticism in that it presents the Old Testament God and Jesus as separate, rival, entities. The logical basis for the belief is that there are contradictions between God and Jesus. Those contradictions prove that Jesus was sent by a different God. Anything that relied on the Old Testament was also wrong: the 4 gospels that are cannon today, the pastoral epistles and the letter to the Hebrews.
There's an answer on your other question that explains this pretty well.