I live in Long Island and work in NYC for the past 16 years. I have not paid any NY city tax and NY SUI/SDI. I just started a new job and they deducted both from my pay check. I know for sure I don't have to pay NY City tax but please confirm I don't have to pay NY SUI/SDI neither? Thanks.

It seems to me that the NY SUI/SDI assessment is a state tax, not a city tax.

Since Long Island is a part of NY state, these taxes would apply.