Reflecting the types of governance, there were generally three layers of law enforcement in the nineteenth-century West:

For a community there was legally incorporated as a city, there was generally a local police force, often with its own jail and occasionally with its own city court system (although this was rarer).

A county had a sheriff (with deputies), with its own jail and with a county court system.

In addition, the federal government (called the "general government" before the Civil War) had federal marshals assigned to territories and/or regions.

That's the basic structure of law enforcement; let me know if you have questions.