I recently bought a pitbull terrier mix puppy. She is 2 months old. Do I need to have permit even for a mixed pitbull?

I think it depends on if you call it a pitbull or a terrier. There is lots of dogs that have pitbull in them that dont have to be registered.

It also depends on what city you live in

Whts it mean by have a permit for a pitbull and why?

Depends on were you live however in most cases oven if it's part pitbull it is usually a no.