You can only get child support in New York from the date a petition is filed going forward - not backward.
Under the rules governing the conduct of attorneys in New York it may be necessary to remind you that this answer could be considered attorney advertising.
Child support is retroactive only to the date that the petitioner files his or her application. That means that, in this case, the mother will not be awarded support for the past 16 years.
Let her continue to threaten to petition for child support. The more time she spends threatening (without actually filing) will be less time that your brother is actually liable for support.
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In terms of the paternity petition the court will look to see who if anyone the child already considers to be dad and whether your brother has provided any support for this child. Your brother should just wait to see if and when she files a petition. She only will have 5 years more tops to claim it. If she isn't on assistance the. She is the only one of the two likely to file.
The above answer does not constitute an attorney client relationship and/ or retention of counsel. This answer is based upon the facts presented and may change if additional information is provided. The rules of the Bar for New York State may require me to advise that this could be construed as attorney advertisement.