Work that an employer "permits" is compensable and a good faith dispute is not a defense to payment. So this is illegal. You could file in small claims or hire a lawyer for a modest fee to file a civil complaint in Kings County Supreme.
I suggest contacting the New York State Department of Labor to get assistance in collecting the wages you are owed.
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You may have claims under the NY State Labor Law/Wage Theft Prevention Act. If you prevail in Court, you may also be entitled to attorneys’ fees, liquidated damages, interest, and costs.
I trust that you kept a log of the work you did, in a journal at home, and have copies of the documentation that you indicate proves your position.
Seek legal advice ASAP from an experienced employment lawyer, who will help you assert your rights while ensuring that your job is not compromised as a result of doing so.
-Denise K. Bonnaig