New York Laws
Article 18-B - Representation of Persons Accused of Crime or Parties Before the Family Court or Surrogate's Court
722-D - Duration of Assignment.

ยง 722-d. Duration of assignment. Whenever it appears that the
defendant is financially able to obtain counsel or to make partial
payment for the representation or other services, counsel may report
this fact to the court and the court may terminate the assignment of
counsel or authorize payment, as the interests of justice may dictate,
to the public defender, private legal aid bureau or society, private
attorney, or otherwise.