Was Jesus a Jew?

Sorry, no cigar.

Mary's husband Joseph was a Jew (means of Judah) of Davidic descent, and Jesus was his legal son (Luke 3:23; literally: son-by-law).

But Jesus' human genes came from Mary, who was a kinswoman (=niece) of Elizabeth (Luke 1:36), who in turn was a Levite (Luke 1:5).