I was introduced to this “potato that grows above the ground” on an organic farm tour in Dominica. It was one of the plants we were most excited about, but because we only got the Patois name (and it turns out I heard that wrong, too), were never able to identify it. Davin and I spent hours searching various spellings, and even guessed at what it could be (a yam) with no luck.
And then just like that Davin found it! Dioscorea bulbifera, aka “air potato” is an African yam (of course) that produces potato-like bulbils along the vining stems. There’s quite a bit of controversy around the plant because not all varieties are considered edible. Many uncultivated forms are very bitter if not poisonous, and there is some debate about how to prepare it to make it safe.
The plant is currently considered an invasive threat in warmer parts of the United States. It’s a very fast-growing vine that can grow up high into large trees and disperse itself easily via the bulbils.
For all of these reasons, the air potato is one weird edible that I would advise against growing.