Who pays for the paternity test to prove the child isn't yours?

You pay

Is the question how much OR who pays? In NY if the mother brings a prospective father in for testing and he is not the father, she pays.

It has to be done at a facility recognized by the Court, and in my area the cost is between $225 and $275.

It depends on the circumstances and jurisdiction. Generally, if a woman is claiming you are the father, then she or the court will pay.