No. Neither your teacher's pension nor Social Security are taxable by New York state.
Most NYSLRS pensions are subject to federal income tax.
Your federal tax withholding is the amount of federal income tax withheld from your monthly pension payment.
Your 1099-R tax form shows the taxable amount of your NYSLRS pension and is provided annually for filing your taxes.
NYSLRS pensions are not subject to New York State or local income tax. If you permanently moved to another state or if you spend more than 183 days in that state, your pension may be subject to state or local income taxes.