Antigonus is a new world quest in the new area Enkanomiya in Genshin Impact. Enkanomiya is a new location introduced in Version 2.4 and brings tons of new world quests like this one to the table. Be sure to switch to Evernight before beginning this quest.
The world quest is located here. You’ll have to glide over the edge of the cliff a bit to see the quest giver. It’s hard to see, so you might have to glide around a couple of times.
The beginning of the quests will have you talk to the two ghosts pictured above. After you finish here, you’ll be sent to another location to find an NPC named Antei. Antei is located in the area below. If you’re having trouble finding him, you can use the teleport waypoint, then walk north. You’ll see him in a slit below.
Antei will have you find a Ruin Guard’s core, and then find an abandoned Ruin Guard. Just follow the indicated locations. You’ll have to defeat this Ruin Guard. After it’s destroyed, you can then collect the book “Before Sun and Moon.” (This book is also required for another world quest, Collection of Dragons and Snakes.)
Return to Antei and turn in the book. This is the conclusion of the Antigonus quest. You can now turn in the Before Sun and Moon book for the Collection of Dragons and Snakes world quest. You’ll receive 40 Primogems and some other rewards for your troubles.