Judaism long ago determined that Jesus himself was a fake messiah. The Jewish Sanhedrin found Jesus guilty and demanded that the Romans execute Jesus. As I read this report it appears that The Israeli Antiquities Authority has taken the position that the evidence is fake, not that Jesus, Joseph, or James are fake.
What actually happened was that Judaism split into those who believed in Jesus being the Messiah (the first Messianic Jews) and those who didn't. Modern Judaism comes from those who didn't believe in Jesus. You still get Jews deciding the become Messianic Christians in modern times -- my sister-in-law being one of them