I asked a question about the growth on my cacti earlier in the summer, however it's just acting weird. I initially thought it was a cacti fruit because it originated from a flower I tried to cross pollinate. But it's looking strange to me, and I'm not really sure what my cacti is doing?!
This looks like a pup and I've seen quite a few of my cacti do this. It's inevitable for branching types as they'd have no means of growing otherwise and I haven't seen it on barrel types like this one, but I can't imagine there is any cause for concern. It's possible it's doing it in reaction to an injury - did you accidentally rip off an areole? - or some balance of nutrients, light, moisture etc it wouldn't see in nature.
You could probably snap or cut it off once it's grown a bit more and grow a clone, if you wanted.
This is an offset or a new branch. The plant looks like a Mammillaria of some description.
These don't always show up in the most aesthetically pleasing locations as you can see. Removing them allows you to root them and have another plant. Unfortunately, the distortion from producing the offset and the scar will permanently mark the plant.
I would leave it alone, personally.