My husband wants to give up parental rights to a child he has never seen or spoken to. The child is about 14 yrs old and he pays child support, however he does not even know the mother,or if the child is his it was a one night stand. Can he do this? If he needs to get a DNA test how does he go about it? What does it cost? He does not know where they are.. just shells out support money, we are in New York State

Why does he want to give up his rights? He'll still be paying child support, unless there is someone who wishes to adopt his child.

I find it amazing that he did not ask for dna testing to start with if as he claims it was a one night stand... Yet he was and still is paying child support? I find this hard to swallow and yes I think in your place I be leery of that red flag.
He can call the child support office direct I am sure they will tell him where he can go to get the test done. Also adding that it wouldn't matter what the cost to clear this up.. But I think he is well aware who the father is or he would not have been so willing to pay.
I don't know hun but if I was you I would start asking some questions to him.

First of course 14 years ago was when he needed to ask for a DNA test, and depending on the state you live at will determine if he can still ask for a DNA test, He should be able to, but some states have rules as to time frame and the such.

He needs to ask for that, if he is still allowed to at this time.

Next, it is of course only his fault he has not seen the child in 14 years and really not a very good comment on him, since if someone had a child, they should want to be a parent to them.

But since he does not see the child, does not have anything to do about the child, why give up rights he does not use anyway.

By the way giving up rights does not take away his obligation of paying child support.