How long would it take to expunged my record in new york state?

The short andwer to your question is it will take forever, literally, as NY law does not permit for expungement of criminal records. Your best option may be a relief from civil disabilities... much luck

New York Criminal Procedure Law 160.50 permits the "sealing" of cases where charges were dismissed, vacated, set-aside, not filed, or otherwise terminated. Otherwise, New York does not allow expungements, or "sealings," of cases where a conviction was entered, except for some older controlled substance, marijuana, and loitering offenses. Sealing a record under 160.50 will prevent the public from having access or seeing the records, including fingerprint cards, photographs, court entries, and other information related to the case. The record may still be made available to some entities, such as courts and law enforcement.

New York also permits the expungements of non-criminal dispositions (violations and traffic infractions, such as disorderly conduct) through New York Criminal Procedure Law 160.55. Misdemeanors and felony adjudications are not eligible. Therefore, you would not be eligible to have this matter expunged.