Live in NJ, Work in NY, Taxes only taken out of NY
I moved from NYC to NJ in Aug. 2020. Right after, I started a job in NYC, for which only NYS deducts taxes. At the same time, I worked a second job (freelance but I get a W2) that switched the tax deductions from NY to NJ once I gave them my new address. (I had another job in NY at the start of the year + NY unemployment that ended right before I moved out of NY.)
It's my understanding that NJ gives credits if you live in NJ but work in NY and pay NY taxes. Is this always the case, or only if my job took out taxes from both NY and NJ? Only about 1/3 of my entire wages for the year were earned while a resident of NJ, but the vast majority of that was taxed by NY, so I suspect I should owe something to NJ, but am trying to understand how the credit for taxes paid to NY works.