How to screw the edge of a sheet of drywall where there is no stud directly behind it?
Unfortunately you are past the point where you could have installed a stud in that corner as a nailer. What you are saying is that you have unsupported drywall butting into the corner now. You certainly can try a longer screw, but be careful not to bend the drywall as the screw tightens. There is going to be a tendency for that corner to wave if you screw it to wall "B" diagonally. Can you still remove that piece of rock and put in even a small 1 1/2 X 1 1/2 nailer, then reinstall the drywall? 

Regardless, use fiberglass tape in this corner if unsupported and the seam will have less tendency to crack. I can almost guarantee the corner will crack if you use paper tape.

I really think you should take the time to install a corner nailer now. It may take a couple of hours to fix the situation, but that is better than  looking at a cracked, wavy corner after you have invested your time and money, knowing that you could have done right the first time.