We’ve learned how to say you’re sorry, but sometimes you don’t need to go quite that far, you just need to say “excuse me” or “pardon me.” In that case consider the Persian verb بَخشیدَن (bakhshīdan), specifically the command form, بِبَخشید (bi-bakhshīd). This is the typical way to beg pardon in Persian, although grammatically it has the effect of kind of commanding that the other person pardon you, which itself seems like something for which you’d need to beg pardon.
Of course, as with many things Persian, there’s also a way to get at this problem using some borrowed Arabic. If you read my Arabic entry on this subject, you’d find that the root عذر (ʿaẕara) means “to excuse” or “to absolve,” and that someone who has been excused can be called مَعذور (maʿẕūr). مَعذور can be combined with a few Persian verbs; combined with داشتَن (dāshtan) it can mean “to excuse” (as in “to have an excuse”). The Arabic مَعذرَت (maʿẕrat), from the same root, is also sometimes used in Persian, particularly with the verb خواستَن (khwāstan) where it can also mean “to excuse,” in a phrase like مَعذرَت خواهی (maʿẕrat khwāhī); you might also see عذر خواهی (ʿaẕr khwāhī), although that shades closer to an apology.
I would stick to بِبَخشید if I were you.