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.
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.