I moved from NYC to New Hampshire at the end of April. When doing so, I changed by address with my employer; however, the information on the w-2 did not change and NY was still being credited for 2023 after already having moved out of the state. As a result, I am now owing more for NY.
Is there a form or any other way to fix this?
Yes. I see 2 interpretations of your question. You should file a NY part year return either way.
1. You left NY, did not work there, did not have NY source income. You will file NY as a part-year resident and only claim the income actually earned in NY. If the state wants to investigate, you have moving paperwork and can prove that you did not live there.
2. You did still work and have NY source income. Therefore it is all taxable to NY. Since NH taxes interest and dividends rather than wages, you would not receive a credit on the state return.
For more from NY see here.
For more on entering states see: How do I file a part-year state return?
There is another possible wrinkle:
Did you work remotely for your NY employer after your move to New Hampshire? If you did, and if you worked remotely for your own convenience rather for the convenience of your employer, then your remotely-earned income would be considered NY-sourced and would be taxable by NY. This is known as New York's "Convenience of the Employer" rule. The rule is explained in detail in this NY tax reference: