Underpayment Correction time limit NY

My last paycheck of 2021 had an insane amount of FICA taxes withheld. Let’s say 3k paycheck and 2k FICA taxes withheld. This was for sure a major overwithholding error, I contacted HR immediately and they agreed this was their mistake and would correct it by the end of the year. This was 12/24 (merry Christmas we stole your paycheck)

They have supposedly corrected it on my W2 and confirmed I should be getting roughly an $1800 payment to make me whole. Only problem is they are saying they’ve already closed payroll for the next period (1/10) and they will not be paying me my missing $1800 until the next payroll date of 1/25. Alternatively they can send me a prepaid debit card overnight and I can have my money tomorrow. I of course immediately declined the payroll debit card because that’s fishy as hell.

They assure me that since I was “paid the wages” but they were just incorrectly withheld this will not affect my taxes if the payment comes next year.

This is a huge multinational company and not some scammy business owner. I’m located in NY.

I hate asking this in Reddit but I’ve been googling all day and can’t find an answer. It seems to me they should not be able to withhold my pay due to their error for over a month, I promptly informed them of the error on 12/24, they closed payroll for 1/10 without fixing the error. It seems extremely sketchy to me that they will send me a debit card right away but have no capacity to cut me a check right away.

Is there a time limit for an employer to correct a payroll error? Can I file a claim for damages?

I’ve been in contact with them all week and had some rather heated conversations stating they need to correct it and a debit card is not an acceptable form of compensation. This resulted in the current stand off ( before they basically said we know it’s wrong and we’ll get to it when we get to it).

What are my options to force them to stop withholding my pay.

Thanks and sorry for the rant.