I live in the bronx my landlord lives upstairs. I paid my rent on the first every month. I told her that I might be moving. I paid November rent and on the 21 of November I inform her that I was moving out the first week of November today is the 4th and she still telling me that I still have to pay her rent and she has my security. I'm moving out this Sunday nov,7do I still have to pay rent knowing she still have my security

Yes the way it works is the security is not considered rent.
If you don't pay you get evicted but you want to move anyway.
I do believe that it can ruin your credit if you don't.

Ok your dates are confusing. You say you told her on the 21st of November you were moving the first week in November. You also say you are movng on 11/7. That's not possible.

I'm going to assume you were on a month to month lease. In that case, you need to give at least one full rental period as notice. So if you told her on 11/21 you were moving you would be responsible for the December rent.

A landlord needs to have some time to find a new tenant and prepare the apartment for them. So giving her a week or two as notice doesn't cut it.

The security is to protect the landlord against necessary repairs. While the landlord can choose to apply the security towards unpaid rent, that's their decision not yours. So pay your December rent.