Can I refuse my son's father visitation rights till he is a fit father?

Initially it is important to know if there is presently any court order in place regarding parenting time between the biological father and the child. If so then you must comply with those orders until the orders are modified. If not then you should make decisions based upon the best interest of your son. The biological father may always file with the court requesting orders regarding parenting time, and even with your particular set of facts there is no guarantee what a judge or hearing officer may order. You should consult with an experienced family law attorney in your area to review all these facts and circumstances, and decide what steps are appropriate for you to take.

You need to request mediation if you have a custody order. If you were or are still married you should file for.

If there is a visitation order in place, you would have to prove that he is unfit to the court.

All you can do is go to court and ask for a custody order that restricts his visitation. Without a custody order, he has the same right to the child as you do. I suggest you talk with a local attorney about the issue.

Not until you change the court order. But based on the facts you might be able to change the court order.

You can not withhold visitation if there is a court order granting the father access to the children. you can be held in contempt of court. However, if the situation rises to such a level that the children are in danger then you can call child protective services or the police. Based on the facts you presented you should file a Motion to Modify the Court Order. If there is no court order then you can withhold visitation because there is no set time that the father is entitled to visitation. But by withholding visitation, that will most likely force the father to go to court to get visitation.