i live in NJ and work in NY. but turbox tax doesnt count the tax i already paid to NY state and says i didnt pay anything to NY state. where to correct it.

You enter your tax paid to New York when you enter your W-2 form in the federal section of TurboTax. It will be the amount in box 17 of your W-2 form. You need to make sure there is "NY" in box 15 so the tax will be applied to New York.