Proceed to obtain an order on consent from the Family Court pursuant to a custody petition. Use or at least consult a family law attorney to do it most efficiently and correctly.
If you found this "helpful" or "best answer," please click it with my appreciation. My response is for educational purposes and does not constitute legal advice nor creates an attorney client relationship which requires all the details and a personal conference.
File a petition with the Family Court in your county. By going to the Petition window in the courthouse, a clerk will be assigned who will assist you in filing out the application and explain the procedures for serving her. Then on the court date (usually about 4-6 weeks later) the Judge can generally give you a custody order if the mother is consenting. In any event, for a full assessment, I'd advise to schedule a consultation with a NYC Child Custody lawyer.
* If you found my answer to be "HELPFUL," or the "BEST ANSWER," please feel free to mark it accordingly.