The small/early hours
Definition 1 of 1
Pro Tip 1/3Quietude
The phrase often implies a time of silence and low activity in the day. 
The streets were deserted in the small hours, with only the sound of a distant train.
Pro Tip 2/3Late Activities
It suggests activities done unusually late, such as studying or partying. 
The students crammed for the exam into the early hours.
Pro Tip 3/3Personal Time
It can indicate private, undisturbed time for introspection or hobbies. 
She treasured her painting time during the small hours of the weekend.