It is not a sprite, and it is not an effect of the hat. What you are seeing is someone wearing a Mastery Amulet. Have you ever wondered why you can't use Power Pips for spells that are not your schools? Well, the Mastery Amulet lets you use Power Pips in a different school. That school's color flies around you when you are wearing the amulet.
"When the battle gets deadly, summon a Death Shield"