If I work for a state mental hospital and it has gotten so dangerous the patients hit us often, can I quit and get unemployment?

You likely will not be allowed benefits. You will need to show the following: First you discussed the problem with your employer, and asked for reasonable accommodations. Emphasis on reasonable (what another would think reasonable, you do not get to decide this). Secondly your employer must refuse to make reasonable accommodations. Then and only then will you be entitled to receive unemployment, but only if GA DOL agrees that your accommodation request was reasonable. More than likely, DOL will say that it goes with your job, and can not be accommodated. Your best remedy is to find another job before you quit.

Possibly. Contact the unemployment office or an attorney.

You can quit, but it is doubtful you will get unemployment. Find another job and then quit.