Books like Innate Magic by Shannon Fay

"Even if a magician's powers surface of their own accord, he will soon be dead if he does not gain the knowledge of how to control them."Alone among all the novices in the Magicians' Guild, only Sonea comes from lowly beginnings. Yet she has won powerful allies—including Lord Dannyl, newly promoted to Guild Ambassador. But Dannyl must now depart for the Elyne court, leaving Sonea at the mercy of the lies and malicious rumors her enemies are busy spreading . . . until the High Lord Akkarin steps in. The price of Akkarin's support is dear, however, because Sonea, in turn, must protect his mysteries—and a secret that could lead a young novice mage deep into the darkness.Meanwhile, Dannyl's first order to resume High Lord Akkarin's long-abandoned research into ancient magical knowledge is setting him on an extraordinary journey fraught with unanticipated peril—as he moves ever-closer to a future both wondrous . . . and terrible.

Maerad is a girl with a tragic and bitter past, but her powers grow stronger by the day. Now she and her mentor, Cadvan, hunted by both the Light and the Dark, must unravel the Riddle of the Treesong before their fractured kingdom erupts in chaos. The quest leads Maerad over terrifying seas and vast stretches of glacial wilderness, ever closer to the seductive Winterking — ally of her most powerful enemy, the Nameless One. Trapped in the Winterking's icy realm, Maerad must confront what she has suspected all along: that she is the greatest riddle of all.

In a world where everyone possesses magical abilities, powerless twelve-year-old Abby, an Ordinary, is sent to a special school to learn how to negotiate a magical world with her unmagical "disability"--and to avoid becoming a victim of kidnappers, carnivores, and goblins ready to prey upon the Ords.