Hello ~ Sorry to say, but your bf has every RIGHT to know this child IF in fact he is the father. The mother of the child says she doesn't want anything from him, but the STATE will decide otherwise. If your bf IS the father, the STATE will make it mandatory that he pay child support, whether the mother wants it or not! That's true in most states, if not ALL.
IF your bf is the father, he SHOULD petitition for parental rights. This child DESERVES a father in it's life! Since this happens ALL the time in this country, so many children have no father in their lives, and it effects them tremendously. My granddaughter is in THERAPY today because of it, and she's lucky!!! 99% of these kids don't GET therapy.

They have to grow up knowing that their father didn't give a darn about them.
So if your bf has any conscience at all, since HE helped MAKE this child -- he will make SURE he's in this child's life if in fact he IS the father. The mother CANNOT keep him out of the child's life, by law! All he has to do it petition the court -- and if she keeps him away from the child, she can be in deep trouble, and even LOSE the child.
You should be supporting your bf in this, as you COULD be a good step mother to this child if it IS his. Give him the support he needs - don't worry about the relationship now. God bless and please take care. Hugs, Lee