Yes. New York requires you to be fingerprinted and a background check. This is done through the company that New York has authorized. You may obtain your fingerprints throughout New York at IndentoGO locations. Preregistration is required. The fee to be finger printed is $101.75 (subject to change).
Registration Website (Preregistration required)
Tip: Try to plan your fingerprinting after you pass your exam and immediately before you apply for your license because the fingerprint data is available to the New York Department of Financial Services for only 45 days. See here.