If it was in fact a temporary custody order, you can probably ask the Court to revist the case and enter a different order based on more complete evidence. It would be best for you to obtain an attorney to assit you. At a minimum, you need to have witnesses at trial who can testify to their observations of his medical condition and more importantly, how it affects his ability to care for the child. Your daughter may be able to testify to give her opinion to the Court if she is of a suitable...
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You said you are divorced and there is no court order. Unless you are paying under an obligation set out in a Separation Agreement, you have no obligation to pay.
Unfortunately, the ability to see the child and the obligation to pay support are separate issues. One does not affect the other. However, he can file a motion to modify his support payments. An attorney would be best able to help him do this, but if he cannot afford one, he can contact the local child support enforcement office and they will have preprinted forms he can use to proceed pro se.
North Carolina courts will not allow a parent to "sign over" his parental rights without a judicial hearing to determine if there is a statutory basis for that parent's rights to be terminated, and whether it is in the child's best interest that this occur. This legal process is called a Petition to Terminate Parental Rights (TPR). A family law attorney practicing in your area can help you. At a minimum, you should consult an attorney about at least getting a custody order if you do not have one.