The phrase "fitful sleep" means sleeping in a way that is not continuous or uninterrupted. It refers to a restless or disturbed sleep where a person may wake up multiple times throughout the night. Full definition
Gardner nodded into fitful sleep, dreaming he was in a warm shower, only to wake to his frozen reality. (si.com)
The second night passed much as the first night in fitful sleep until I woke just before the sun rose when the bus ground to an unwelcome halt. (theexpeditioner.com)
So I get up to teach this morning utterly spent, only having had about 3 hours fitful sleep, very little preparation time, and emotionally weak and vulnerable. (nakedpastor.com)