1 - Get a Written Agreement

The very first thing you should do - if you do NOT already have a child support order for that 1st child - is to have a written agreement drawn between you & the mother of that 1st child. The agreement should be drafted by a capable child support lawyer, as there's particular language which should go in there so it's valid.

2 - Ideally Get the Agreement Reduced to the Form of an Order

You are best advised to then file a petition in Family Court & get a Support Magistrate to issue a court order based on the agreement. Then if the mother of the 2d child files a petition for a support order, you can produce a copy of that agreement and/or order, along with proof of payment, and you should receive a credit for supporting that 1st child.