Wiktionary
patrilineality
n. 1 (context uncountable English) The condition of being patrilineal 2 (context countable English) Such a descent or kinship
Wikipedia
Patrilineality
Patrilineality, also known as the male line, the spear side, or agnatic kinship, is a common kinship system in which an individual's family membership derives from and is traced through his or her father's lineage. It generally involves the inheritance of property, rights, names, or titles by persons related through male kin.
A patriline ("father line") is a person's father, and additional ancestors, as traced only through males.