The quarter back squat can be used as a squatting variation when pain or injury precludes full depth squats, or as a way to overload the legs and trunk in particular with weights beyond what a lifter can squat.
 
Back squat until the knees are near a 90-degree angle, ensuring the position is identical to what it would be at this point of a normal back squat. Don’t sit the hips farther back or shift to the heels to make it easier. Stay shallower as needed to avoid pain if using to work around injury.
 
Drive directly back up without allowing your chest to lean forward or your weight to shift to your heels.
  Purpose
The quarter back squat can be used to overload the top of the squat movement in order to strengthen the trunk or to strengthen the legs and hips for the final pulls of the snatch and clean. It can also be used as a temporary squat variation for lifters with pain or injuries that prevent full squatting.
 
Programming
The quarter back squat can be programmed as the back squat would be if being used as a temporary back squat alternative in cases of injuries. If being used to overload the top of the lift, sets of 3-5 reps at 90% of the back squat and above (potentially over 100%) can be used.