If a stranger sleight of hands a feather into one of your player's hats/helmet, does that feather count as being worn or carried by the player? If so or if not, can a spell like darkness be cast on that feather?
If the point you choose is on an object you are holding or one that isn't being worn or carried, the darkness emanates from the object and moves with it. Completely covering the source of the darkness with an opaque object, such as a bowl or a helm, blocks the darkness.
What about an arrow that was fired and lodged into an enemy, or an object being held by your own mage hand? (Mage hand is not a concentration spell.)