| You will receive a credit on the NJ return for the state income tax you pay to NY on your wages. However, as with anything involving taxes, it is not quite that simple.
If you live in one state (New Jersey) and work in another (New York) you must first pay state income tax to the state in which you work (New York) on the wages earned in that state. The non-resident state (New York) will not directly tax you on your other income (i.e. NJ wages and self-employment earnings, interest, dividends, capital gains, etc.).
The state where you live (New Jersey) will tax you on all of your taxable income from all sources, including wages earned in another state (New York). Your resident state (New Jersey) will allow you to claim a credit for any non-resident state income tax paid to another state (New York) on income taxed by both states.
You will have New York state income tax withheld from your wages. You will probably not have New Jersey state income tax withheld.
It is a little confusing, but there is no reciprocal agreement between New York and New Jersey.
Shirley | 
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