Your federal return is always done first. Since you are in TN, without a state income tax, there would not be a first for states. Normally, if you live in a state that has an income tax and work in another you file the nonresident state and then the resident state. Since you live in TN, the NY return would not be relevant.
So since you live in a state without income tax, you would just file the NY nonresident return IF you do not meet the Convenience of the Employer Rule. Otherwise, you will only file your federal return.
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