Pay you receive while serving in an area designated as a combat zone is exempt from New York taxes. Your deadline for filing a New York return, paying tax due, or filing an amended return to claim a refund is also automatically extended at least 180 days after your last day in the combat zone or contingency operation, or after your last day of hospitalization for an injury suffered there. Any days left in the previous filing period when you entered the combat zone are added on top of the 180 days.
There is nothing to apply for. Leave your combat zone pay out of the income you report on your New York State return, and file within the extended deadline if you are using it.
Your orders and Leave and Earnings Statements showing your combat zone service dates, and hospital records if you are counting hospitalization time toward the extension.