Scathing Mage is a light armor set. When you deal direct Critical Damage, you have a 20% chance to increase your Spell Damage by 516 for 6 seconds. This effect can occur once every 6 seconds.
The Scathing Mage set is part of the Imperial City DLC. It drops in Imperial City Prison in the Imperial City. Each set item is bound on pickup. You can acquire light armor, weapons and jewelry of this set in the Xivkyn motif style.
If you need more information about the Imperial City, make sure to check out the full Imperial City Guide