Once you have accepted a new job, you have accepted it and it becomes your last employer, regardless of whether or not it is as well paid as your old job or whether you got approved for benefits after being fired from the old job. If you quit this job, regardless of reason, and file for unemployment benefits again, (which is called "re-opening" your claim)you'll have to use this job as your last employer. And when you voluntarily quit a job, except in the rare case of having a very excellent job related (not personal) reason to quit the job, you will not likely be approved for unemployment benefits again.
And if you quit the job and try to just re-start your unemployment without telling them about this new job, you're going to be committing fraud, the system will catch you, and you'll be asked to pay back the money you may have received with penalties. So that's not an option either.
In most circumstances, unless you are in a particular type of system sponsored educational program, you are not allowed to attend school full time and draw unemployment benefits, which you draw because you are out of work for a reason not your fault, and are able, available and actively seeking a full time job. Keep the job you have now, try to flex your school schedule around it, or find a job that you can do and go to school. But getting back on unemployment insurance is probably not going to work out for you.
