Is it legal to pay child support in a different state kids live in?

Your question is a bit confusing. What would be illegal about it? A parent is required to pay child support to be financially responsible for their children, upon a dissolution of the marriage, or where the parties are not married, in a paternity action. Once a court order is entered it  is entered, it is enforceable and given full faith and credit under the laws of the United States. The answer to your question is certainly yes. Even though your children may reside in a different state than you do, you would still be required to pay child support for them.