If you enter federal taxable interest income, it will appear as taxable on your state return unless you instruct TurboTax to exclude it. You will see an option for this on the screen that says Tell us if any of these uncommon situations apply:

Also, if you enter federal exempt interest, you be asked which state the exempt interest belongs to.

So if you think too much interest is being taxed on your New Jersey state tax return, you need to reveiw your interest income entries in the federal section of TurboTax.
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