If you have already purchased NY software for the desktop, use that instead of Online. Online is going to charge you for federal and both states. Open the federal return (w/ NJ resident) you did file through the TurboTax desktop. Add the NY nonresident return (i believe you already purchased the desktop software for NY) and allocate all of your wages (assuming you only worked in NY last year) to NY. You will owe the state of NY so you will have to pay them directly. The NJ return will need to be amended to add a credit for the tax you pay to NY, so you will eventually get a refund from NJ.
You are dealing with 3 different tax agencies (IRS, NYS, and NJ state) and one won't take payment from either of the other two. The NJ will have to be amended because you have not added the credit for tax paid to NY yet. You won't know how much credit you can take on the amended NJ return until you complete the NY nonresident return. Use the desktop to add NY and change the NJ return since you already have paid for the software.
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