Exiled Unjustly is one of side quests in Elex. During it you can help an exiled woman called Katta to return to a village after she was unjustly accused by the Berserkers of being a thief.
How to unlock this quest: Speak with Katta on Berserker Island.
Berserker Island is located on the south end of the map and this place is presented in the picture above. You can swim there and when you reach your destination, you discover a fishing village. Speak with Katta and learn that she was unjustly exiled from Goliet. You can help her reclaim her good name.
Go to Goliet and speak with Alrik (200XP) who came up with a plan that can help Katta and exonerate her. This plan will also accuse the real culprit, Drog. Collect 3 Claws from Alrik, you can also get Alrik’s Keyring from him but this is optional (if you won't ask for them then you will have to use Lockpicking ability).
The first part of the plan is to break into Born's and Sinda's chests. Sneak into their homes during a night (this allows you to stay undetected). Then, use Alrik's keys or Lockpicking ability and open the chests. Take Born’s Valuables and Sinda’s Valuables from them. However, that is not all because you must leave 1 Claw in each one of them. This will help in accusing Drog of being the thief. Select the second tab (placing items inside of containers), find the Claws in the hero's inventory (the picture 1), select one unit and use the option to place the item inside of the robbed person's chest (the picture 2).
The second part of the plan is to place the stolen valuables inside of Drog's chest to which you must also sneak. Place 1 Claw, Born's Valuables and Sinda's Valuables. The "final" content of the chest is presented in the picture above.
Lastly, go back to Alrik and inform him that the preparations are complete. Drog is accused of thievery and Katta can go back to Goliet (200XP). You can meet with her – she guards the main entrance to the village. You receive 1000XP, 114 Shards and Katta’s Claw (a quest item – it is connected to the Claws' hideout in Domed City – more details can be found in pages with the descriptions of A Strange Mechanism and On Behalf of the Claws quests).