Kiri Wazawa’s on-going The Morose Mononokean (Fukigen na Mononokean) is a Japanese contemporary-fantasy manga. Volume 1 collects the first four issues, first serialised in Square Enix’s Gangan Online magazine.
On Hanae Ashiya’s first day in high school, he took pity on what he took to be a discarded toy in danger of being squashed by foot traffic. The “toy” was no toy but a fuzzy demon, which immediately latched onto the hapless boy. With his lifeforce rapidly dwindling, Ashiya is beyond the aid of any mundane succor.
Luckily for Ashiya, his high school has a resident exorcist whose mystic ads Ashiya can see.