Yes, you will file a New York nonresident return in addition to the NJ resident return. New York has, in addition, a "convenience" law that affects those who telecommute, or work from home, for NY companies. Income earned from your home on behalf of a company operating in New York is considered taxable by New York. This website https://www.citylab.com/transportation/2014/03/end-twisted-law-taxes-telecommuters-twice/8584/, discusses this law. Depending on what your W-2 states, your entire income may actually be taxable to both states (check with your employer on this, to see if they have filed documentation that states your work from home is for their convenience and not for yours).
You will want to prepare the New York return first, whether it is for 27 days or the entire year, because NJ taxes that amount also. However, NJ will give you a credit for the tax you must pay to NY on this same income. Therefore, you prepare the NY return first so that the credit is accurately calculated in TurboTax. In addition, the NJ return will ask you a question about double-taxed income. This is the same as the amount of income that is attributed to New York.
Here is an FAQ about nonresident returns to assist you: https://ttlc.intuit.com/replies/3302052
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