A Hearth Witch at Chisolm Keep

Misha Millik is a hearth witch, brought by Headmaster Winterton to Chisolm Keep, a school for magic. She's a misfit, surrounded by wealthy children, her only friend a stray cat. She is desperately unhappy and completely inept at any kind of magic the school teaches. But Winterton insists she is where he wants her. How can she succeed and find her purpose?