@z3 thank you.
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@OP You should apply online for NY unemployment right after your last pay check arrives. New York Dept of Labor will hold your unemployment payments until they see that Citi paid the severance after the 30 days which I guarantee they will. You should get the severance in around 6 to 8 weeks after your last pay check. Truth is, the later you get the severance, you are guaranteed to get your unemployment payments. They will give you forms to fill out, you will be called down in person as well to show proof of Identification etc, but after that you should get the severance + the unemployment payments. Expect to be called down to the Department of Labor 3 consecutive times once you are collecting as they want to see all your work effort forms, etc. Good luck.
The NYS DOL has a FAQ page about this: https://dol.ny.gov/dismissalseverance-pay-and-pensions-frequently-asked-questions