If you are an employer as described in federal Publication 15, Circular E, Employer's Tax Guide, and you maintain an office or transact business within New York State, whether or not a paying agency is maintained within the state, you must withhold personal income tax.

Out-of-state employers who are not incorporated or licensed under New York State law and do not maintain an office or transact business in New York State are not required to withhold New York State, New York City, or Yonkers income taxes on employees who reside in New York State.

If an out-of-state employer agrees to withhold New York State, New York City, or Yonkers income taxes for the convenience of the employee, then the employer is subject to New York State withholding requirements.

Employers should withhold tax for the following employees:

(1) New York State residents earning wages even when earned outside of the state;

(2) New York State nonresidents being paid wages for services performed within the state;

(3) New York City residents even when services are performed outside New York City;

(4) Yonkers residents even when services are performed outside Yonkers;

(5) Yonkers nonresidents on wages paid for services performed in Yonkers.

Please note that If you changed your New York City or Yonkers resident status during the year, complete Form IT-360.1, Change of City Resident Status.

Employers paying wages or other payments subject to New York State withholding must file a return and pay the New York State, New York City, and Yonkers taxes required to be withheld. All employers required to withhold tax from wages must file Form NYS-45, Quarterly Combined Withholding, Wage Reporting, and Unemployment Insurance Return, each calendar quarter. If you withhold $700 or more during a calendar quarter, you must file Form NYS-1, Return of Tax Withheld, and remit the tax due, within 3 or 5 business days after the payroll that caused the accumulated tax withheld to equal or exceed $700.

[Reference]:
https://www.tax.ny.gov/bus/wt/whtax_require.htm
https://www.tax.ny.gov/bus/wt/filing_requirements.htm