The fact that the 8th amendment was ratified in 1791 means there must have been jails at the time. And if there were jails, there must have been government agents responsible for making arrests. But the first police force did not appear until nearly half a century later, and that was only in Boston.
Who made arrests in 1790s America? Who ran the jails?
Sheriffs were the government agents charged with pursuing, arresting, jailing, and providing those arrested for trial which first started in the 1630s in what later became America (in both Virginia and Plymouth in 1634, with Plymouth also having a constable since 1632). Once in the courthouse the magistrate (or justice) was in charge.
I answered [How were laws in America enforced before police/slave patrols?] (https://www.reddit.com/r/AskHistorians/comments/h9xi2f/how_were_laws_in_america_enforced_before/) not too long ago which expands on all forms of colonial and early American law enforcement and their roles. I'm happy to answer any followups you may have.