Why did unemployment deny my claim - NYS Department of Labor gave no clear reason

Section 593 usually relates to work history or wage requirements. Did you work enough quarters or earn enough wages in your base period? You need to have worked at least 2 quarters and earned a minimum amount. Check your monetary determination to see if your wages were reported correctly by your employer.

same thing happened to me last year, turned out my previous employer contested the claim and said I quit when I was actually laid off. You might need to appeal this and provide documentation that you were laid off not terminated for cause

You have 30 days to appeal this denial. Before you do that, call NYS Department of Labor and ask them to explain exactly why you were denied. The phone system is terrible but you need specific details to write a proper appeal. If you can't get through on the regular line, there's actually a service called Claimyr (claimyr.com) that helps people reach NYS Department of Labor agents when the phone lines are jammed. They have a video demo at https://youtu.be/qyftW-mnTNI showing how it works. I used it when I had an adjudication issue and got through in like 20 minutes instead of calling for days.

DONT GIVE UP! The NYS Department of Labor denies tons of valid claims hoping people wont appeal. I got denied twice and won both appeals because I had my paperwork in order. Get your termination letter, pay stubs, anything that proves you were laid off not fired.

might be worth checking if your employer reported your separation reason correctly too, sometimes they put down 'quit' instead of 'laid off' and that can cause automatic denials