What should I do about my doubt regarding paying the subscription fees for a Qur'an memorization center, and is it permissible to give in charity an amount equal to the subscription value to get rid of this doubt?

If the center does not allow the admission of participants except after paying the fees, then this is an indication that you have paid the fees, and you should not pay attention to this doubt so that you do not open the doors to obsessive thoughts upon yourself.