It depends. If you have leased an apartment for 12 months, did you live there for the entire tax year or did you travel back and forth to FL? Since you rented an apartment, if you spent more than 184 days in NYC you are considered a resident since you have a 12 month lease which counts as a permanent abode.
If you are working your remote job while living in NYC, then yes, the earnings you receive from the remote job in FL will be taxed by NY State and NYC.
If you are living part time in FL and part time in NY, then you would file a Part Year NY resident return. NY starts with your federal income, even as a part year resident, and then makes adjustments. On this return, you will adjust and deduct the income you earn WHILE in FL that is NOT from a NY source. So, if you have spent 100% of your working hours in NY, then you would be taxed on 100% of the income. If you spent 20% of your remote hours working while in NY, then 80% of your remote income would be excluded from your NY return. All of the income you earn working part time in NYC would be taxed to both NYC and NY.
NY Residency
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