Antigonus is a new world mission in the new Enkanomiya area in Genshin Impact. Enkanomiya is a new location introduced in version 2.4 and it brings tons of new world missions like this one to the table. Make sure to switch to Evernight before starting this mission.
The world’s mission is here. You’ll have to slide a bit over the edge of the cliff to see the quest giver. It’s hard to see, so you may have to slide a couple of times.
The beginning of the missions will have you talking to the two ghosts shown above. Once you finish here, you will be sent to another location to find an NPC named Antei. Antei is in the area below. If you’re having trouble finding it, you can use the teleportation landmark and then walk north. You will see it in a slit below.
Antei will ask you to find the core of a Ruin Guard and then find an abandoned Ruin Guard. Just follow the indicated locations. You will have to defeat this ruin guard. Once destroyed, you can collect the book “Before the sun and the moon.” (This book is also required for another world quest, The Dragon and Snake Collection.)
Go back to Antei and hand over the book. This is the conclusion of the Antigonus quest. You can now submit the Before the Sun and the Moon book for the Dragon and Snake Collection world mission. You will receive 40 Primogems and some other rewards for your troubles.