He has no rights to my knowledge. Meaning he has never signed the birth certificate. My son has my last name. There is no dna or child support order. Can he legally walk up to my door after so far 3 months and want visitation. Or can I say no go away. And does he have any legal right with the info given above.

Yes, he has rights. Does he know this child exists? Does he know where you live?* (*I just reread your title.)

He can legally ask for a DNA test to be done to prove the child is his.

Where did you get the idea he has no rights? He has the same rights as any father, the only difference is he does have to go to court to enforce those rights. Until he does, you can refuse visitation. However, it will not look good in court if you do.

ANY question on law needs to include your general locale as laws vary by area.