My daughter lives with her mother and she is going to move out on her own at age 18. Right now she is 17 and I pay her mother support for her, but do I have to continue to pay her mother if my daughter moves out and on her own and starts working? What does the law in NY State say about this situation?

If she leaves the mothers home and is out on her own then you could ask the courts for relief by granting her emancipated. When she moves out and if she has a permanent residence then file for child support to be set aside. Then if she stays out of the home and turns 21 ask that child support be ended. If she has a child before turning 21 you can petition the courts for the same thing.