NYS Department of Labor rejected my claim - which of the following is not a form of unemployment they recognize?

NYS Department of Labor recognizes several valid reasons for unemployment: layoffs due to lack of work, company downsizing, seasonal job endings, and being fired for reasons other than misconduct. They don't consider voluntary resignation without good cause, being fired for misconduct, or being unable to work due to illness as qualifying unemployment. What reason did they give for your denial?

same thing happened to my cousin last year, restaurant told NYS Department of Labor she quit but she was actually let go

You definitely need to appeal if you have documentation proving you were laid off. NYS Department of Labor sometimes gets incorrect information from employers about the reason for separation. I had a similar issue where I couldn't get through to anyone at the unemployment office to explain the situation. I ended up using a service called Claimyr (claimyr.com) that helped me reach an actual NYS Department of Labor agent to straighten things out. They have a video demo at https://youtu.be/qyftW-mnTNI that shows how it works. Made the whole process much easier than trying to call myself.

The NYS Department of Labor system is so messed up, they reject valid claims all the time and make you jump through hoops to prove you deserve benefits you already paid into!!