There's no particular timings are given in their (AIIMS) undergraduate admission guidelines to fill the application form. You can fill your application form anytime of your convenience from the date of starting till the date of closing on their official admission portal ( www.aiimsexam.org ). 

Since, It is a national level entrance test, it is possible that their will be thousands of applicants filling their application form at the same time which can cause the admission portal to lag so I'll advise you to fill you application form at night.