So I have a question I have sole legal and sole physical custody,when I filed.I was trying to be nice and leave reasonable visitation,because I always tried to get the father to see his son,well he didn't show up or make effort so I was awarded full custody,well since then he has made even less effort than before and seen him like once every four months,now last time he seen him was thanksgiving,its not healthy for my son,and when he did see him he cried and wanted nothing to do with him because he didn't know who he was,what I'm wondering is there anyway I can just completely close the case,possibly stop him from having any rights,because he really doesn't care about his son,as I said before he shows no effort at all and I think it is my sons best interest that he doesn't have a father figure like that in his life,its not healthy please help

No you can't remove his rights unless there is an adoption going on. Even with limited contact the courts may allow him visitation of some sort.

So can I ask him to give up his right can he try and get custody at anytime witch I dpubt he will but I have say if he sees him or not

Again, no! There is this myth that a parent can just give up their rights. But it is only a myth. Only a court can terminate parental rights and courts are VERY reluctant to do so. The prevailing thought of family courts is that a child is better off with 2 parents. Therefore, they want to bend over backwards to allow both parents to be a part of a child's life. If you ask for a TPR the answer you will almost definitely get is, the other parent isn't using their rights so what do you gain by taking them away?.

So, from a practical standpoint, the only time a court will terminate parental rights is to clear the way for an adoption or if the parent is a serious danger to the child. Until the former happens or you can prove the latter, don't waste time and money trying to terminate his rights.