Blue Exorcist / Two Worlds

Doctor Kurona Akumu's father mysteriously went missing while writing the last chapter of his manga/anime Blue Exorcists. Kurona goes to his office and is shocked to see a scene of the dying Rin Okumura, the main character of Blue Exorcists, on her father's computer. While reading a note left behind by her father, a hand from the monitor pulled her in and she finds herself on the rooftop of a building next to a bleeding man. She manages to save him and realizes that the person she saved was Rin Okumura. Kurona later discovers that she can only leave the manga/anime based Rin Okumura's change in feelings. When that happens, the words 'to be continued' will appear and she will teleport back to the real world. It's the story of two people who live in the same era but in different worlds.
Rin Okumura is always picking fights with delinquents unlike his more studious younger twin brother Yukio Okumura. He is surprisingly hired for a part-time job but gets fired after he encounters a hobgoblin that wreaks havoc in the store. The next day, he encounters a demon that causes his dormant demonic powers to awaken. His guardian, Shiro Fujimoto, saves Rin and reveals that he is the son of Satan born from a human.