Hello,

Do I have to give any notice when asking my daughter's father who has been living in my apartment since Nov 2008 and is not on the lease at all nor does he pay rent to leave.

Yes, you have to give him a written notice that his tenancy is terminated and he must move out within 30 days.

Even though he is not on the lease and hasn't paid rent, he has established residency and must be treated like a tenant. If he doesn't move out at the end of the notice period then you can file a lawsuit to evict him.