Most states (CA being one...) don't cross reference social security numbers.
That's an IRS --> Social Security Admin function.
You should still (probably?) amend the NJ return to correct the issue, but I doubt the return is going to be rejected. But them there right coast states do things differently. 😀
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My thinking is that it will be rejected. Not because NJ cross-check the SSN but because NJ is a piggyback state (unlike CA, which is a Standalone) that must pass through the IRS and the IRS should catch the mismatch.
Was the Federal return accepted?
Still an AllStar