Charging a Previous Employer's Account

My question involves unemployment benefits for the state of: Calif... I worked for a new employer for only 6 months and was let go due to no fault of my own, can the California unemployment department deny me if I quit the previous employer? The previous employer does not want their account charged for my unemployment since I quit that job to start the new job? In other words, will the state deny my unemployment since I quit the first job, and only worked the second job for 6 months before getting fired?

This one's kind of a long answer, but with 6 months employment, you will most likely have earned/worked enough wages/hours to have purged a disqualification from your prior quit regardless. In the event your former employer can't avoid the charges to it's reserve account, they might offer you your old job back to do an end run, and then if you refuse it, create a refusal of work issue that might get you disqualified.

To prepare yourself, get educated on "suitable work" if there's any chance you don't want to work there again.

The longer answer is that even if you didn't have enough earnings to purge the disqualification, leaving a job for a "better" job is usually considered a compelling reason to leave so even if you only worked the new job 1 day or the new offer was rescinded before you actually worked there but had already quit, you could still get UI.