Legal Question in Criminal Law in California

You posted this question under criminal law, but you asked about filing a lawsuit. Such a suit would be civil, not criminal. The actions you describe doo sound like a crime and, like many crimes, would also justify a civil lawsuit. But if you want this person to be prosecuted, you need to report what happened to the police. Hopefully you did so at the time of the attack or soon thereafter.

Now let me turn to the question you actually asked.

That the employee was "on the clock" does not necessarily mean that his employer is liable to you. But even if it isn't, you have a viable case against the employee personally.

The employer is liable only if the employee was acting in the course and scope of his duties when he hit you. Obviously, his duties don't include punching customers. But the analysis is not that simplistic. I would need to know what he was doing at the time as well as the surrounding circumstances before I could answer your question one way or the other.

Even if the employer is liable, you can also sue the employee.

Note, however, that you're not likely to receive a very large judgment even if you win. You probably have not incurred significant medical bills, and may not have incurred any at all. You can recover general damages (meaning damages or the attack itself, unrelated to the extent of your injuries) as well as some damages for pain and suffering and compensation for certain out-of-pocket expenses you reasonably incurred as a result of the attack. Depending upon the circumstances, you might even be able to recover a modest amount of punitive damages. Unless there is more to the story, though, the case may not be large enough to interest attorneys who work on a contingent-fee basis.