The verb miff is an informal way to say "annoy." If your sister's constant humming is starting to drive you crazy, you can tell her it miffs you.
Long ago, the word miff was also used to mean "huff" or "pique," so you might have described yourself as "in a miff" about your sister's tuneless humming. These days, you're more likely to see the adjective miffed describing someone who's irked: "I am so miffed that none of my friends came to my party on time." Experts guess that miff comes from the annoyed sound you might make when you're really miffed.