Judaism is more than a belief in God and Jesus. If that is your definition of Judaism it is faulty. Traditional Judaism does not believe in Jesus other than maybe he existed. But they do not acknowledge him as the Messiah, his resurrection, or as a Savior unto eternal life through faith in him or by any other means.
Judaism in the NT period became a case of believing Jews attempting to combine the two religions, demanding that the Mosaic Law, the Torah, be kept in addition to believing in Christ as Messiah and Savior. The apostles dealt with it on a regular basis as we see in Acts, Corinthians, Col. etc. In that respect Judaism still exists, though there are many definitions of what Judaism is, some not even connected to religion but ethnicity.
The religion of Israel in the OT influenced Christianity, yes. It was the forerunner to it before Christ's birth, life, death, resurrection, ascension. It laid the groundwork for his arrival. Both are monotheistic, but only Christianity is Trinitarian in its understanding of God as existing uniquely as Father, Son, and Holy Spirit, equal in essence--- ---one God, not three.
The NT interprets the OT. Jesus and the apostles were doing this all the time. Things that could not be fully revealed in the OT are revealed in the NT and through Christ.