As I understand, the Jewish faith, is passed from the mother’s side but as to actual lineage, Jesus, though only Son of His Father, was Jewish, both fully man, to understand us, yet fully God to forgive us.
As I understand it, in Biblical Judea, the Hebrews traced lineage primarily through the father.
Among the Diaspora, it became pragmatic: Many people fornicated, and had children out of wedlock. It was obvious who the mother was, not so the father.
(This was also the understanding of my Hebrew teacher, a native Israeli from outside Tel Aviv.)