You need to file a non-resident MA return, showing zero MA income, in order to have the incorrectly withheld MA taxes refunded to you.
I suggest you file the MA return on paper, and attach a letter of explanation.
For the coming year, if you keep the same job and your employer will not or cannot withhold NJ taxes, you may well want to start making quarterly estimated tax payments to NJ.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
