I work remotely from home in NJ. A new employer withheld NY taxes. Is this correct?

If you work remotely for a NY-based company for their convenience, your income is not considered NY income.  But if you work remotely for your convenience (in other words, the company has a office you could work at in NY, but they permit you to work remotely) then the income is NY income.  Here is the tax memo listing the rules and factors to consider.

https://www.tax.ny.gov/pdf/memos/income/m06_5i.pdf

You would file an NY non-resident tax return to report and pay NY tax on your NY-source income. You will file a NJ resident return for all your world-wide income.  You will get a credit on your NJ return for out of state taxes you paid.