See this web page for multiple data sets related to corrections.
You can search for a demographic with the search on this page. The search results will be a list of many reports, which must be read through individually.
Browsing through the menus is also useful.
Finding data here will take time; be patient and diligent.
See: Annual Survey of Jails: https://www.bjs.gov/index.cfm?ty=tp&tid=12
"Established in 1972, the National Criminal Justice Reference Service (NCJRS) is a federally funded resource offering justice and drug-related information to support research, policy, and program development worldwide."