I am a NJ resident who works in NY City. I received a payout from my mother's 401k after she passed away. I list that on my federal income when filling out my NY State Tax return. When Ny State calcluates my taxes they are taxing me on more income than I made from my job in NYC, it seems that they are taxing me on money that I received from my mother's 401k as well. This doesn't seem right because my mother lived and worked in NJ. How can NY state tax me on more income than I made in NY state?

No, that was an error on NY state's part.

Amend the return and redact out the 401K money from the NY state return. Since you live in NJ, NY has no claim on that money.