Which Tanakh verses support the halacha that tribal affiliation is transmitted through the paternal side?
In the Talmud-GemaraTractate Bava Bathra 109b
משפחת אב קרויה משפחה אמשפחת אם אינה קרויה משפחה דכתיב (במדבר א, ב) למשפחותם לבית אבותם
The Family of the Father are family the family of the mother are not family as it is written with regards to the Tribal census in Numbers 1,2(one of the 24 books of Tenach): "according to their families through their fathers house"
In Bemidbar 26, the B'nai Gilad argue against allowing the daughters of Zelophad to marry outside the tribe of Manasseh given that the landholdings they were awarded (due to their father passing away without leaving a male heir) will become property of the tribes they marry into.