Imperial City, Temple District
White-Gold Tower; Green Emperor Way, Shattered Void
The Shadow Cleft
Dreloth Ancestral Tomb
108669 (Imperial City)
134263 (Unfinished Dolmen)
235758(?) (White-Gold Tower)
Grievous Twilights are powerful winged Daedra found mostly in the Imperial City, and are a corruption of the common Winged Twilight. They have the ability to teleport and often use it to outflank their enemies.
During the related quest, you must kill Grievous Twilights for their claws. so you can create a concoction that will protect relics of the Imperial Temple from being destroyed by the Daedra.