My daughters father and I have been to court and have court documents stating that he is to have visitation every other weekend and we also have a child support case. I do understand that one thing has nothing to do with the other but since then he has failed to pay child support going on a year now and has moved out of state. I nor my child have seen or heard from him for the last almost 6 months. She is very young and my concern is that he will eventually try to come back and try and use his "some what" rights to have access to her. They do not have a relationship at all as it stands now and I see no point in having an "every other weekend" order.

You would go back to the court the issued the order and file a petition for modification of the custody order. You would cite his lack of visitation as the reason. The clerk of the court and tell you what documents to use, but CANNOT give you legal advice. You may want to retain an attorney, or ask a local legal clinic for assistance if you are not comfortable doing it on your own. An attorney is a MUST if he has one though.

It will depend, I know here in GA, unless there is a major change in the situation, you can not get a modification ( at least in Fulton County Court) for two years.

But please understand, so you go back, and he shows up to fight it, and wins, then what ? But even if you end up with him only get a number of weeks in the summer perhaps because of the move, he can always go back to court to ask for it to be modified again, in two years or four years or more. So a modification now is good for now, but they are free to change or ask for a change also any time in the future, if they move back to the area or have a change in heart.

He doesn't have an attorney. From the looks of it he doesn't have much of anything. I have been trying to get back to court with it though. Is this a Superior Court issue or Civil?

I don't have many worries about he himself fighting it because he just wants to get out of the child support obligation but his mother is another story. Don't get me wrong I do not want to keep my child from knowing her family. I do still make sure that she gets regular visits with his mother. What I want is the right to protect my child from any furthur heart break later on. The problem isn't as simple as it was put. Her father has been very difficult to deal with and has brought more drama into our lives than I can even speak about. (well he and his family). But even with all that said, it ios not my intention that he does not know his daughter. It is my intention that his rights to her be limited to what I feel is a safe and comfortable place at least until he gets his own act together. This has been an on-going battle for too long and like I said at this point we have not seen or heard from him in over 5 months until his mother approached me about taking my daughter 5,000 miles away to visit with him. My answer was of course no but I want to make sure that I have myself covered in case they choose to fight it. He already disregarded court and fled the state, I do not want him or his family to be able to leave the state with my daughter as the laws in that state and this differ. I will not run that risk.

Depending on where you live this is neither Superior Court or Civil Court, but rather Family Court.

Depending on where you live this is neither Superior Court or Civil Court, but rather Family Court.

As J_9 says, this depends on where OP is. In many states, there isn't a separate court entitled "family court". Assuming the Superior Court in your jurisdiction is a trial court (as opposed to an appellate court), it would probably be responsible for both civil (perhaps including, but not limited to family law issues such as divorce, child support, and custody) and criminal cases. Thus the title of the court would probably not be "Civil Court".