The crucial protocol of squatting is to push through your heel when moving upwards, this allows to transfer all the weight that you are carrying to your leg muscles which is exactly what the intent of the exercise is!
By wearing running/sport shoes which are generally cushioned and are a common choice for all of us to wear to the gym, the purpose of the exercise is not fulfilled. The load that we carry while squatting gets distributed to the knee, lower back and other injury prone areas apart from the leg muscles?
So what should we do to maximise our results and avoid injury at the same time?
When you’re squatting, a rigid sole is best so that the heels can drive into the floor as much as they can, so try wearing flat shoes such as football trainers or weightlifting shoes.
OR
If you do not want to invest in another pair of shoes just for squatting and are happy with the shoes that you currently wear to the gym, then you can go ahead and squat barefoot!
Now do you know why most powerlifters prefer squatting with no shoes on? It might not be comfortable initially but you will get used to it soon?
Just make sure to be safe from the heavy weights that are lying around (especially at our indian gyms) when squatting sans shoes?