Fate Seekers appear in the Harabah Block within Tartarus, from floors 191 to 200. They will make frequent use of their Maragion skill.
Persona 4
Fate Seekers will appear alongside other Shadows in Chapters 2 through 4 of the Void Quest within the Midnight Channel. They are immune to Physical attacks and will simply use their spells to attack. Upon being defeated, they may drop the Gazing Clasp material. Selling 6 Gazing Clasps at Daidara will unlock the Inversion Fan ougi for Yukiko Amagi.
In Golden, it may also drop Howlite for trade at Shiroku Pub.
Persona Q: Shadow of the Labyrinth
Fate Seekers are powerful Shadows that ambush the party at P-Spots in Evil Spirit Club Stories 3 and 4 and are rarely encountered on Story 4. It will spend a few of its turns "thinking", choosing to throw a Rakunda or a normal attack. After a while of thinking, it will have "made up its mind" and start fighting at full force, usually beginning with a Bestial Roar to get the jump on party members in subsequent turns.
Equipping Phys-resistant armors and using Fang Smash can help the party weather its standard attacks, but keep the party health high to avoid getting destroyed when it chooses to drop a Megido on them.
If killed while inflicted with the Cursed ailment, it will drop the Monitor Eye rare material, which is required for the request, Obtain an Evil Eye.