That looks very much like there had been some baseboard there that either wrapped around the wall and returned into that gap, or perhaps there was trim on the stair stringer that wrapped into that gap.
I'd suggest that the easiest way would be to replace that with a new piece of baseboard that will fill the gap. Of course, this means that your new baseboard would have to be this tall.
Another option would be to put a small piece of wood in that spot to "widen" the apparent width of the stair stringer. It's hard to tell from the image provided whether the stringer (and quarter round above it) sticks out beyond the wall board, or if they're flush.
If they're flush, simply put in a small piece of wood that matches the height. Don't install it with the end-grain showing - it will split far too easily when you try to nail it. Instead, install it with the end-grain out, and drill pilot holes for the finish nails to go through.
If they're not flush, install a piece of the baseboard trim running uphill with the stringer, and a piece horizontally with the drywall. This will likely fill most, if not all, of the gap.