On the following page of our guide to Greedfall, you will find a description of Inquisition side quest.
Where to start the quest?: San Matheus, reading the letter outside the house.
After accepting the assignment, go to have a conversation with the Natives who live in a forest near San Matheus. You will be directed to search the Inquisitor Claudius' house. Go to the indicated place and pick up a letter from home. When you leave home, you will come across a group of inquisitors - temporarily, there will be no fighting.
Now go to the office of the Inquisitor Claudius. As before, find the chest and open it to find the man's notes. Run to the natives now and tell them everything. The Inquisitor will appear - throw yourself into battle and fight him. After winning the fight, talk to the natives and you'll complete the task. You will be rewarded with + 2 reputation with the Natives faction and gain 1600 XP.