Jinsei Zenbu Kakete mo Gin no Majo ni Kachitai

Story

Family lineage, appearance, honor. And magical talent. The earl's daughter Fran had it all — until the day she suffered a crushing defeat at the hands of a silver-haired girl named Cruel, at the age of ten. Five years after they vowed to have a rematch, the two rivals reunite at a magic school. But things are far from what Fran had imagined — rather than facing off again, she discovers that Cruel suffers from a rare condition that prevents her from using magic without receiving mana through "physical contact," leaving her on the verge of expulsion.

Synopsis via AniList (English).