Jesus was born into a family of practicing Jews dedicated to Judaism. As prescribed in the Torah, he was circumcised on the eighth day after his birth. Throughout his life he was thoroughly committed to Judaism, the Torah and Jewish practices. He prayed in synagogues and taught Torah to “multitudes” of fellow Jews. And John the Baptist only baptized Jews to purify them for the expected arrival of the Jewish Messiah. All this is stated clearly in the Gospels.
The word “Jew” appears 202 times in the New Testament and 82 times in the Gospels, while “Christian” does not show up at all in the Gospels and is mentioned only three times in later parts of the New Testament — the first mention is when Paul is preaching in Antioch years after the crucifixion ("And when he found him, he brought him to Antioch. So for a whole year Barnabas and Saul met with the church and taught great numbers of people. The disciples were called Christians first at Antioch." -Acts 11:26).
There was no such alleged thing as Christianity until long after Jesus died, and neither he nor his disciples invented the term, it was applied to his disciples (promoters) by others.