This could get complicated. What is your husband's state, or states, of permanent residence, and what dates did they change?
For now, I will assume that your spouse's state of permanent residence for part of 2023 was California and then he changed it to New York. In general, if you file a joint federal return and joint state returns, you would be required to treat him as a full year resident of NY, and a part-year resident of CA, meaning he will pay tax in CA on income earned in CA but he will pay tax in NY on all his income for the year, so he would possibly pay some double taxes (there may be a credit to mitigate this). And, you would also have to file jointly in CA, meaning you would pay CA income tax on your income even though you never lived or worked in CA.
One solution to this is to file a joint federal return but file the state returns as married filing separately -- you file MFS in NY as a full year resident, and he files MFS in CA as a part-year resident and in NY as a part-year resident. That way, CA only taxes his income for the days he was a CA permanent resident and NY only taxes his income for the days he was a NY permanent resident.
Since you filed the state returns jointly, and it is after the deadline, that can't be changed to MFS at the state level, you are stuck with filing MFJ. Maybe CA has a way of excluding your income even on a joint state return, but I don't think NY has a way of excluding his income.
It's not clear to me how your state returns were filed and what income was reported in which state. Start by reviewing that. It may be that the "part-year resident" designation was created by you accidentally when you reported his change of residences and filed a joint return. In which case you need to check some things -- was your income taxed in California when it shouldn't be? And was only half your income taxed in New York instead of all of it? If only half his income was taxed in NY, that was probably also incorrect. On a joint return, all his income should have been taxed, although he would be eligible for a credit for tax paid to CA on the same income.
That's the landscape you need to be looking at. I can't think of a good way to provide specific help being both anonymous and only communicating by public forum. I suspect you will need to see a tax professional to review your situation and help you correct the NY return (and possibly CA as well).
Then lastly, because amended returns take a long time to process, I don't see any way of getting the additional Empire credit any time soon. You will have to watch the news and check the state tax department web site. It is possible that there will be a way for people who did not get the supplement in August to add it to their 2024 tax return, so it adds to the tax refund for people who did not get the direct payment. But you will need to watch the news and forms.
https://www.governor.ny.gov/news/governor-hochul-announces-350-million-direct-financial-assistance-l...
