State tax filing

You should enter your W-2 on the federal screens as it shows on your W-2. 

Then, complete your New York nonresident return first. On the New York Income Allocation screens, you will specify how much of your income was earned in NYS. Please make sure you follow the instructions as follows to get to the correct screens:

1. Open your NYS return.
2. On the screen New York Income Allocation, select no for the question about earning all of your wages in New York State.
3. Answer yes to the question, Did you have any New York State Wages?
4. Enter the wage information.
5. Enter your allocation method for your wages. If you entered the "$40" amount in Step 4, you can allocate it as 100% New York State Income. 
6. Your New York return should show just your allocated NYS wages under the NYS amount column as shown in the example picture attached.

Once you complete your New York return, you can do your resident return. Although New Jersey will tax you on all of your income, they will give you a credit of taxes paid to New York. Please see How can I calculate the other state tax credit as a New Jersey resident who works in New York? for more information.