Seirei Gakusha Kidan Reikyou Kaden Story
From Doko Demo Doa Manga Scanlations:
Yuika Aoi has a recurring nightmare in which she isn’t able to save a mysterious, green-eyed man called Rei. Her elderly grandmother, who was born in the Taisho era, lives very traditionally, and at times seems to have magical powers. Apart from all this, she is a normal high school girl until she falls off a roof and into the Taisho era, in the middle of a battle between Rei and a fairy. Will she be able to save him this time?