The overhead squat demands a high amount of midline stability, and therefore a high amount of core stability.
Given that this movement requires you to hold a weighted bar overhead, much of the stability work will go to the core, most predominately the lower back. If you do not have an active midline when performing the Overhead Squat, you are disposed to hyper-extending the lower back, resulting in an unfavorable overhead position—AND putting yourself at risk of injury. It is therefore imperative that you strengthen your core muscles and mobilise your lower back as often as possible.
You surely know these exercises to strengthen your core, but try this one to improve it even more:
Paused Overhead Squat