What is the law regarding visitation of a noncustodial father of child 4 months of age?

I don't think there is a blanket law.

I think it's determined on a case by case basis in court when setting up partial custody and visitation schedules.

Yes there is no "law" some fathers will get full custody, somme fathers get joint and equal custody, others get visitation on weekends and certain days during the week. Others will have to get only supervised visits.

It can depend on what type of father he can be, it depends on the state if in the US, it will even depend on which Judge you get.