Can the father of my child legally keep communication between me and the child

I would need a lot more information to give an accurate answer to your question.  But if you and the father were never married (and there are no court orders about your child) and he is keeping the child from you, it is advisable that you file a Paternity Action to establish child custody and visitation.  In the meantime, you may be able to have the Sheriff or Police accompany you to the father's residence and show the birth certifcate that you are the mother, and if he has no court order granting him custody, then law enforcement may ask him to return the child, unless there is some indication you are unfit as a parent.