If my employer wrongfully withheld New York City Residency tax for me, how do I get this money back when filing my taxes?

[DanielV01]

This will be taken care of when you file the NY state return.  When you file the state return, you are given credit for both the state and city taxes withheld.  However, when you are a NYC nonresident, your NYC tax portion on the state return is $0, so the NYC taxes withheld increase your refund.

To illustrate:  let's say you had $3000 of NYS taxes withheld, and an additional $1,000 of NYC taxes.  When you prepare your NYS return, you are given credit for paying $4000 of NY tax.  When you prepare your NYS return, let's say your NYS tax is $2500, which would entitle you to a $500 refund of NYS tax withheld.  However, your NYC tax is $0.  So your refund will be $1500 instead of $500.

NYC tax is reconciled on the return along with NYS tax.  If you don't have to pay NYC tax for not living in the 5 boroughs, any city tax withheld from your paycheck will be included as part of your NYS income tax refund.