Some of these will be free and some will require a subscription. Many of these sites, such as Ancestry, have a TON of free databases to search in (they call them catalogs). And often if there is a catalog that you have to pay to access on one site, it may be free on another. So don't fret!
United States Court Records - https://www.familysearch.org/wiki/en/United_States_Court_Records
Newspapers are a GREAT resource to find information about criminal activity. It is usually the one resource that kicks off the adventure of learning about your criminal ancestor.