My baby is 16 weeks old what rights does his father have for contact where and how long for. And he also has 2 other children also not living with him I don't believe he is able to care for all at the same time as our baby has gastric reflux and a query food intolerence and is not well a lot of the time. We where not married or living together. And he has already missed maintence payments

First, please pay more attention to posting guidelines. There is a Read First sticky at the top of the Children forum (where this was moved from) which directs questions of a legal nature here.

First, have you gone to court to establish custody/visitation? You discuss maintenance payments so it appears you may have some court orders. Is he asking for visitation?

Laws are generally not specific about this. But generally courts will allow only visits with the mother until the child is weaned.