My ex husband has not seen our daughter in 3yrs can I sue him for abandonment and being absence in her life? We live in NC. He does pay child support. Also will the court order me money since he only pays child support.

You do not "sue" for abandoment, that is a criminal issue. The term is also used in civil cases but for the reason to ask for a modification of your custody agreement.

So, what type of custody agreement do you have. What type of court ordered child support is there, how for behind in actual court ordered support is he

Custoy agreement is joint. And child support ordered is by the divorce court which he pays on time each mo. Being divorce for 8yrs.

No there is no "more" money unless he is earning more and the order needs to be modified, is he paying part of the health costs, health insurance and other items that are often included.

If not you may try and get a modification for some of those

You may also go and ask it be changed from joint where you have primary legal and physical custody

What grounds do you really think there are for abandonment ? Since he is paying child support there is a consideration by the courts that he is participating in the child's life even though there may not be visitation that is ongoing.