Peevishly is how someone speaks or acts when they are being peevish: in a short, irritated way, over something small. She peevishly refused to wait. He answered peevishly. It is the adverb, so it tells you about the manner, not the person as a type. Same register as peevish: a little bookish, at home in stories and in a teacher’s report, not in a text to a friend. Though actually, learners who know peevish as “annoyed” sometimes stick -ly on and think it means “annoyingly” — making other people annoyed. It does not. It means the speaker themselves sounds cross and hard to please. The feeling is petty, not grand.

不耐煩地；使性子地