On this page of the guide to The Witcher 3: Wild Hunt, you will find descriptions of treasure hunt quests in Faroe Island from the Skellige archipelago. These are minor optional quests related to the Horned Hoskuld's Sword used in a separate side quest, and the Ironside's treasure.
Hidden in the depths
Go to the southern coast of Faroe island and find the body of a castaway (M19,2). Take the letter and the key. Read the note. The approximate location of the treasure will be marked on your map. Go to the marked location and dive. Watch out for echidnas that are nearby.
Use witcher senses, the chest will shine in red. Inside you will find Horned Hoskuld's Sword. Sadly, the sword will be damaged, so you must go to the blacksmith to repair it, but the quest will be completed anyway. The sword is needed for the Iron maiden quest, in which we've described on the page on side quests on the Faroe island.. You can also use it normally.
To start the quest you must reach a small isle North from Faroe (M19,5) and take a book from the body of a sailor. Read the notes you found.
The approximate location of the treasure will be marked on the minimap. Swim there with a boat. Watch out for sirens (level 13). The treasure chest is lying quite deep, so you must watch out not to run out of oxygen.