Formerly, the Fallen Daughter of the Duke, Volume 4 (manga)

Claire Martino once had everything: a loving family, a crown prince fiancE, and a hopeful future using her family's inherited magic. Then, in an instant, she lost it all - and the culprit was her own beloved half-sister. As the daughter of the now-disgraced duke and scorned as a villainess, Claire leaves everything she knows and sets out on a journey to find her true self.

But wait, isn't that the plot of the otome game NEW START ETERNAL LOVE on its hardest route...?