Meaning how did it eventually break off from we call Judaism today? I know it's because Jews don't believe that Jesus was the messiah but where in biblical texts does it specify this?
Biblically, start with Acts of the Apostles in general, and pay close attention to the Council of Jerusalem. Per Acts, Chapter 15, Paul was leading the faction that wanted Christianity to be open to Gentiles, and James (the brother of Jesus) was leading the fact that wanted Christians to be Jews first. And the big points of contention were circumcision and dietary restrictions. Per Acts, Peter gets a vision from God regarding tolerance, and he backs Paul at the Council of Jerusalem, and Gentiles were able to become Christians without becoming Jews first. Galatians 2 refers to the events of the Council of Jerusalem, but Paul glosses over the events.