I don't know NY law, it's probably available on line. In Ohio, you can make an objection before your plea based on defect in the citation.
The state will then most likely move to ammend the ticket. If they do that, you may be able to object if they don't follow the exact procedure for ammending a ticket. In Ohio, you are supposed to be properly served with a new citation - you may be able to object on that grounds if they don't do that.
Look up the code in regard to ammending a citation. Post here if you find anything useful.