Common words:
* patriarch: the male head of a family or tribe
* patricide: the act of killing one's father
* patriotic: having or expressing love for or devotion to one's country
* patrimony: property inherited from one's father or ancestors
* patrician: a member of the nobility, especially in ancient Rome
Less common words:
* patriarchy: a system of society or government in which men hold the power and women are largely excluded from it
* patrilinear: relating to or based on descent through the father's line
* patrilocal: relating to a custom in which married couples live with or near the husband's family
* patrimonial: relating to or inherited from one's father
* patristic: relating to the early Christian Fathers
* patriate: to return to one's native country
* patriot: a person who loves and supports their country
Words related to "patri," but not directly starting with it:
* paternal: relating to or characteristic of a father
* paternity: the state of being a father
* expatriate: a person who lives outside their native country
* repatriate: to return someone to their native country
Keep in mind that "patri" can also be a part of longer words, such as "patrician," and "patristic."