Is there any halachic stance (Orthodox halacha) by which a Patrilineal convert inherits either Tribal status or legal connection to their father?

I remember a previous reply to an old post in which a commenter informed me of the Shulchan Aruch’s position that a Patrilineal convert could be a Posek and/or a Dayan because of their heritage. Is there any legal precedent for Tribal inheritance (status and land claims) or legal connection/recognition of paternity?