From kickstarter update #3:
In the Hired Gun expansion each player will receive a token that depicts their Cowboy Brand. Using this token will increase your influence in the corral it is placed in.
After placing a tile, players may place ONE token (Badge Token or Hired Gun Token) onto an incomplete corral. That Token remains until the corral becomes completed. Once the corral is completed the player receives their token back.
Not sure about "Sheriff" expansion, perhaps you mean "Stinkin' Badges?" Form kickstarter update #2:
Each player receives 1 Badge token depicting a sheriff's badge, with their player-color background. After placing a tile, a player may place a Badge token into an INCOMPLETE corral, covering up a Cowboy Brand. The covered Cowboy Brand no longer counts. After a corral is scored, any Badge tokens in it are returned to their owners.