I cannot speak for the Federal Prsion system, but can for a State Prison. This link gives specifics.
California Correctional Health Care Services - Career Opportunity
The salaries are highest at the prisons with the sickest patients. These prisons have many many sick patients with cancer, HIV, HCV, etc. You can start at $318k per year plus benefits on top of that base for starting board certified time limited. Salaries are about 30k lower in the prisons with healthier populations. There is still a good pension, but it was greatly reduced 4 years ago. After working there for a few months, you also get over 4 weeks a year off with holidays, vacation, and CME. This grows as you put more time in.
You need to accept the realities of working in a prison . While many of your patients are extremely appreciative, there will be times when very bad things happen. Prison riots, homicides, suicides still happen. There are infrequent assaults on staff. And you will get sued. Frequently sued, like 5 times a year. These are managed by the State's attorneys who are good, and for the most part make this manageable.
Years ago, the quality of care was terrible. Now, you are held to very high standards. You will be reviewed frequently for quality of care.
Bottom line, finances are excellent, but not for the faint of heart.