At the Fireside Chat after my Prison and Court Records talk today for the Ontario Ancestors 2022 conference a gentleman asked about finding prison records for Carleton. I do not have specifics as to the time period in which he was researching nor his ancestor's name.
The first thing to keep in mind is that these records will likely not be digitized, may not be fully accessioned or indexed so searching by your ancestor's name will not yield any results.
My first stop would be the Archives of Ontario. Searching for Carleton + jail yields
- Ottawa-Carleton Detention Centre inmate case files: 1939-1957, 1972-1991
- Administrative records of the Ottawa- Carleton Detention Centre: 1860-1991
The second record set seems like a good place to start a search though the Ottawa Jail was a maximum security correctional facility. It includes 61 metres of textual records and 21 reels of microfilm (textual records).
"Series consists of records created and maintained by officials of the Ottawa- Carleton Detention Centre, and its predecessor, the Ottawa Jail, pertaining to the administration of the jail. Records include jail, surgeon's and punishment registers, inmate case files, drug control records, daily count and record books, historical records, and indices."
There are also the County and District Court Judges' Criminal Courts for 1869-1984.
My suggestion would be for the researcher to contact the Archives of Ontario with the specifics in terms of name and date and see if the archives has records to fit his quest. The archivist will let you know if they have records for the place and time period you require or point him to other resources.
Do not forget newspapers — if your ancestor was arrested, it likely made the news.