I believe what you mean is you had New Jersey tax withheld in 2024 even though you didn't live or work there. Since you worked in New York in 2024, you owe taxes there but there was no tax withheld so you owe a penalty for late payment of tax. I don't know of a legitimate way of protesting that with the state of New York, as they were not at fault here. Your only remedy would be to complain to your employer about it.
The New York City local tax is assessed on individual residents, not on businesses, so it is your responsibility, not your employer's.
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