Can my child’s father keep her from living with me and my boyfriend?

Custody and visitation rights are not contingent upon paying child support.  Instead, the best interests of the child will determine who should have custody, where the child should live, and how much child support should be ordered. As the biological father of the child, the child's father could file a paternity suit and ask the court to officially declare him "dad".  In the suit, he could also seek full or shared custody of the child.  If the child has always live with you and there have been no issues, then you will have a good chance of retaining custody (especially since the child seems to be a very young age.)  If there have been issues, like your boyfriend has an assaultive background or you have been reported to children's protective services, then you could be in for a fairly tough custody fight.  No one factor is controlling.  Instead, the court will look to what each parent has to offer the child and who can provide the best environment physically, financially, morally, and scholastically.  If there are issues, then work quickly to resolve them.  It would help if you and the boyfriend were married in the event that you were assigned a judge with strict moral feelings.  However, you should never get married simply for strategic custody gaming.  Only get married if you intend to have a live and family with your boyfriend.  Every judge has a few things that they really like to see parents do.  You may want to considering having a consultation with a family law attorney in your jurisdiction, just to get a feel for some of the pet peeves and preferences of your local judges.  With this information, you can develop a parenting plan that will give you a much better chance of success in a custody dispute.