The chances of him getting custody is very, very slim. However, if he would like to visit, the court, may grant him visitation. If you argue, the court would grant him supervised visits. The best thing you could do is attempt to have your fiance adopt the child. Adoption terminates the Father's rights for custody, visitation, child support...everything. You do not have to get the biological father's permission in certain circumstances. If you would like further info. call my office and have a free consultation.