The tapered edge of the drywall is denser and harder due to the rolling
process that tapers it
It's not on the tapered edge, but very near. I actually had to screw on
the other tapered edge, and there were no problems. I put up 3 sheets
so far, and all went smoothly except this one stud. I'm not going to
hammer the screw into the stud, but try to create a dimple somehow
without damaging the paper.