I am the mother of a 6 mos old & have been the sole caregive. Although the father of my child has purchased diapers & clothes a few times he has not

If you have court-ordered child support, he also probably has a possession schedule. Based on the information you've provided, it's very unlikely that he will be able to change where the child lives. When you consider what a Court would do in a family law case, think about what is in the best interest of the child. Would it be in a child's best interest for a court to send a 6 month old baby to live with a man who has only seen her 3 times? The answer is a very clear "No."  It sounds like the father is making idle threats. However, be sure to continue allowing him access to the child. Otherwise, he could start building a case against you.  The best plan of action is to build a co-parenting relationship with him that allows the child to know both of you. Your relationship with the father may have failed, but the two of your produced a baby together so you'll have to figure out a way to work together in parenting.