The Notorious Virtues by Alwyn Hamilton

At sixteen, Honora 'Nora' Holtzfall is the daughter of the most powerful heiress in Gammamix; her family controls all the money - and all the magic - in the entire country. But when her mother is found murdered in an alley, the family throne and fortune are up for grabs, which means Nora will be pitted against her cousins in the deadly Veritaz trials to determine the rightful inheritor.

But there's a surprise rival in the form of Ottoline, aka Lotte, the illegitimate daughter of Nora's aunt, who was left with nuns as a baby. Thrown into the Veritaz, she is suddenly surrounded by a hostile family she never knew she had.

But as the Holtzfalls wage their battles of privilege, something bigger and more sinister bubbles beneath the surface, and revolution is in the air.

Incredible tests, impossible choices, and deadly odds await both girls. But there can only be one winner.