What to do if I want to go for higher studies during 24 month stem extension period.

i am currently in 24month stem extension period. I am planning to go back to school for a higher education level in fall 2017 (Aug 21). I have only used up 30 days of my unemployment days. When would be the earliest I can quit my current job to stay in the US legally, before I start my classes on Aug 21st?

Well, I suggest you check with DSO at your current F1 status school or DSO at the higher level degree school that you plan to pursue to get correct answer.