I've never heard it. A barb is an insult. Therefore a barb can sometimes be particularly stinging.

That's not a phrase that I've run across very often, and it sound a bit old fashioned to me. A barb is like a sharp point or thorn, so it can also, figuratively mean a cutting insult: https://en.wiktionary.org/wiki/barb#English (meanings #1 and #2) So I'd say for example that someone had a "barbed wit" if they were often saying cutting or mean remarks in a smart or funny way. So I'd maybe interpret that as meaning: that person says insulting things that have a stinging effect.