From what I remember once he got his demon powers he would fight other demons or monsters with that power but he wasn't able to control it until later on. In the ending of the anime he fights someone else who has the same power but is superior to him. The antagonist then took the girl that the protagonist loves, as a hostage so the protagonist can fight him. I think I remember watching this on Netflix.
The anime's it's not: Blue Exorcist, Devilman Crybaby, and Heaven's Lost Property.