I have handled many appeals from denials of unemployment compensation. I have never seen a single instance of denial based on why you left "prior" employment, it focuses on the reason employment with your last employer ended. Therefore the answer is "no," if by "based on a 'prior' job," you mean will they question whether your quit that job, or not, or why.
The job prior to the last one would enter in only in determining if you have enough work credits to qualify for benefits.
If you are denied benefits, contact an attorney about an appeal.