You probably already know how to play this voicing for the G-sharp minor chord:
It is basically using your index finger as a barre across the 4th fret, and essentially the same as using a capo at the 4th fret and playing the basic Em chord:
Try either placing a capo on or using your index finger to barre the 11th fret and play the Am chord:
If you capo or barre at the 6th fret and play the Dm chord, you're actually playing the G#m chord:



