Break up the bar brawl.
The second assignment from Sheriff Marion, right after dealing with poor widow Rooney, is to break up a bar brawl in the Malamute Saloon instigated by two miners from LeBarge's and McGrew's mines. Upon arriving you will find two workers ("Blasphemous" Bette and Caminetto) having a go at it. You can stand and listen to them for a bit (nothing happens if you don't take immediate action), but sooner or later you'll have to break it up.
Talk to either Caminetto or Blasphemous Bette and ask them to stop it, then use either the line about working for Sheriff Marion or load up your guns and wait for target practice. Whatever you do, don't provoke them into a fight - it's bad mojo and the town goes ballistic. If you manage to convince them to break up and take one in, you'll get the option to jail both parties for the time being, which is pretty much the best possible option.
Then, return to Sheriff Marion afterwards.