My ex-wife told my children, neighbors, friends, and through her attorney, my former employer that I fathered several children out wedlock. I received a paternity suit filed by the state welfare authorities alleging that I was the father of a 17 year old with a woman I did not know. I appeared, and learned that my ex had someone go through the state database of public assistance recipients looking for anyone claiming that their out-of wedlock child(ren) were fathered by someone with my name. The woman had letters from my ex, a photo of me, my SS#, birthdate, photos of my children (with my ex) and a mother's day card from my ex! The child is not mine via DNA. What's my recourse? I've lost my job and, I'm devastated by this.
Divorce / Separation Lawyer
If the statements were made within the past year they are perhaps defamatory and could be the subject of a slander action (or if written, libel). However, the cost of such an action could far exceed any recovery.
On the other hand it is possible your ex committed some form of harrassment, which would be a criminal complaint. The problem with that is that in the context of a domestic relations case the police and prosecutors tend not to want to get involved.
Call a NY attorney first and foremost. Each state code on defamation is unique. In Virginia, you would not have a claim unless you have been ruined professionally because of this (can't get a new job etc..)
Sadly, I think the best recourse would be to do nothing. I know that is not great legal advice, but it sounds so personal that nothing good could come of filing suit. Do your kids want to watch you sue their Mom? Probably not.
I am sorry - good luck!