u/okay_okay_okay_

Hi all, I'm mostly a beginner learner and I was wondering what are some common ways to say you're sorry, and the contexts in which you'd use them? Is "Entschuldigung" the standard word? If I wanted to say something more akin to "my bad" (i.e. a quick casual apology), what would be the closest equivalent? Something like "Mein Fehler"? Thank you!