One of the quest in Fallow Mire is In the Artifacts Requisition in the Mire. It requires you to find two artifiacts -Fereldan Medallion Service and the Fereldan Tome. Both of these items can be a loot drop from killing mobs in the map. I killed mobs on the area just west on the Old Mill. The screenshot below will show you. Remember to step on the water to “spawn” mobs.
The archer mobs drop the medallion easily, however Fereldan Tome, you might also want to kill the ‘spirit’ undead mobs.