My job had the wrong state down all year. So I paid taxes to MD instead of NJ, for all of 2019. I have never lived or worked in MD. What do I do?

[TomD8]

First of all, you'll have to file a NJ tax return.   If you were an NJ resident all year, ALL your income is taxable by NJ.

Second, you'll have to file a non-resident MD return, showing zero MD income, in order to obtain a refund of the incorrectly withheld MD taxes. 

[Anonymous]

you need a corrected w-2 to show wages as NJ.

here's what MD says about the error  if you are a nonresident - file nonresident return form 505

MARYLAND TAX WITHHELD IN ERROR
If Maryland tax was withheld from your income, you must

file to obtain a refund of the withholding. Complete all of the
information at the top of the form through the filing status,
residence information and exemption areas. Check the box
provided to the right of the residence information for you to
indicate your withholding was withheld in error. Enter your
federal adjusted gross income on line 17 in both columns 1 and
3 and line 24. Then complete lines 43-47, 49 and 51.
Sign the return and attach withholding statements (Forms W-2
and/or 1099) showing the Maryland tax withheld equal to the
refund you are claiming.
Your return is then complete. You must file within three years
of the original due date to receive any refund.

you are also going to have to file a NJ return.  be prepared for penalties because no taxes were withheld. 

[TomD8]

@Anonymous  -- Presumably the employer has already deposited the employee's withheld taxes with the State of MD.  Therefore the original W-2 is correct.

The employee corrects the mistake by filing MD Form 505 as you described.