N.Y. Civil Practice Law & Rules § 303 (2026)

§ 303. Designation of attorney as agent for service. The commencement
of an action in the state by a person not subject to personal
jurisdiction is a designation by him of his attorney appearing in the
action or of the clerk of the court if no attorney appears, as agent,
during the pendency of the action, for service of a summons pursuant to
section 308, in any separate action in which such a person is a
defendant and another party to the action is a plaintiff if such
separate action would have been permitted as a counterclaim had the
action been brought in the supreme court.