Jinsei Zenbu Kakete mo Gin no Majo ni Kachitai

Fran, the daughter of an earl, had a strong family background, good looks, and magical ability—until she was defeated at age ten by a silver-haired girl named Cruel. Five years later, they meet again at a magic school, where Fran expected to face her rival once more. Instead, she learns that Cruel has a rare condition that stops her from using magic without receiving mana through physical contact, putting her at risk of being expelled.