How old is he. If he is over 18 his mother cannot stop him. Have a DNA test done.
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He will need to file a petition to establish paternity. If he is found to be the father, then he has rights to visitation and/or custody depending on the circumstances. Until then, he will regretfully be at the mother's whim.
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How old is he? If he is over 18, he is free to travel anywhere he wishes to travel. If he is the father of your child, you need to get to court to establish his rights and responsibilities. There is no way the alleged father's mother can know for sure that the child is not his unless she was with you ALL the time. Please speak to a lawyer to help you get this cleared up. If you are under 18, have a parent or guardian find a lawyer for you.