I live and work in New Jersey but my employer paid taxes in Massachusetts

Hi, 

I work for a consulting firm.  For year of 2019  I lived and worked in New Jersey.  But my company somehow paid my state tax in Massachusetts from April-2019 to Dec 2019.  

 

Now my W2 will show that I worked in Massachusetts even tho I didn't work there.  

 

Will I be able to get back all the taxes paid in Massachusetts and pay that to New Jersey?  What are my options now?  My company basically said that there was mistake in their system and there is nothing they can do now.  

 

Please suggest.