How to allow a particular user to take quiz very next day in drupal
I would suggest to make use of rules: 


Create user role (by hand) which always access to quiz let say QUIZER
On Event "I want to enter Quiz"
Look up Time Last entered date from current olr
Check if allowed to go on
Add role quizer to current user
On event "I'm stopping the Quiz"
Remove role quizer from current user
Save Time last entered Quiz in user profile