Leviticus 24:10 speaks of the son of an Israelite woman and an Egyptian man as being “among the community of Israel” (ie, Jewish).
On the other hand, in Ezra 10:2-3, the Jews returning to Israel vowed to put aside their non-Jewish wives and the children born to those wives. They could not have put aside those children if those children were Jews.
There is an extensive section on this in Dueteronomy, too, but I don’t have time to hunt it.
Shabbat Shalom !shalom b'SHEM Yah'shua HaMashiach