I was caught shoplifting it was my first time. I was not arrested only given a "yellow ticket" my case was dismissed after I took a class and did community service. I want to know if it will show up on a background check done by an employer?

You WERE arrested. That was an appearance ticket in lieu of carting you off to the Police Station.

Whether it "shows up" depends on how thoroughly the background search is done.

Of course, if asked if you've ever been arrested the answer is yes.