system
A chat on 4chan
human
Probably an ancestral god, family god, an elemental or a servant. In no particular order. Family gods and ancestral gods doesn't really want worship usually.
gpt
I’d say kitsune but they’re a bit iffy on the worship thing, depends on which one probably. So then I’d just go with the creature you have in pic, the friendly neighborhood dunpeal

>Family god
Never heard of one, what are they?
human
Either of the below:

>A god/goddess blesses the bloodline and becomes their representative deity. This is how kings were selected in ancient times. Ofcourse, god can always pull back their blessings. So family must keep themselves worthy. There isn't much blessed families these days and none of them have any real political power. 

>A family creates a spiritual network in the bloodline and creates an artificial god. This god connects the family together and helps them in life. You can think of it like racial soul but it's smaller. One skill learned by a member will help the other learn it better etc. Also it creates a bond which family members don't backstab each other. Families like this have a lot of political power in local places.