She says it's yours. You know it isn't. After all, nine months ago, you were broken up and you were a Rhodes Scholar at Oxford. Nonetheless, because you were married at the time of conception, the baby is legally presumed to be yours. How do you fix it?
We've all been there. (Maybe.) Especially the Rhodes Scholar part. What you do to fix the problem depends on what stage of the process you are stuck at.
Did you sign a Voluntary Acknowledgement of Paternity Form?
The VAP form is a legal declaration that you are, in fact and in law, the father of the child. It is an irreversible legal declaration that makes you responsible for the child. However, there is one definite loophole. If it has been less than 60 days since the form was signed, you can simply fill out another form to reverse the action. After 60 days, however, there is little to no hope of reversing the declaration.
Were you married at conception, delivery, or when listed on the birth certificate?
If you were married at any of these three critical junctures, you are presumed to be the parent of the child. That means, until you fix the mistake, you are responsible for the child. The solution to this problem is to file a case to "declare the non-existence of the parent-child relationship". That part is best handled by an attorney.
The law requires the suit to be filed within two years of obtaining "knowledge of relevant facts", such as the existence of another man in your baby mama's life or the knowledge that you are sterile.
What if I am not legally the presumed father but she's demanding money anyway?
Call a lawyer. Seriously though, if you are not the presumed father, and have not signed a VAP form to declare that you are the father, it is up to her to prove that you are. That means court filings and paternity tests, or a trip to the Maury show.