The judge in the paternity case won't help. You might put them in a storage unit and send her the key.
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.
It sounds like you have a multitude of legal problems that one or two calls to an attorney could probably rectify.
As far as the letter is concerned, a certified letter indicating itemizing the pieces in your possession that belong to her and giving her a time-frame to come retrieve them (and the consequences for failure to do so) is probably fine, but as you suspect, it has to conform to a whole host of regulations (city, state) unless you want to expose yourself to a countersuit if you fail to give her adequate notice.
As far as the paternity judge question is concerned, maybe? The judge would have to have jurisdiction over the dispute, and based on the facts you've included, it's difficult to answer affirmatively that the court would.
I suggest seeking out a free consultation from a general practice attorney, and see if they can point you in the right direction. A few hundred dollars ought to clear this up, which is a bargain considering the exposure you have if you get it wrong.
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