If you liked
Akatsuki no Yona
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...then you might like
Cross Ange: Tenshi to Ryuu no Rondo
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These two shows are both two-cour series with female protagonists, in settings that take inspiration from east Asian cultures, and they even aired during the same seasons! And more importantly, both are stories of princesses abruptly cast out of their life as royalty, and their subsequent journey. And, Akiko Shikata wrote the soundtrack and insert songs for Cross Ange, as well as the second ending theme for Yona of the Dawn (which she also performed). There are some other similarities as well, but they're possibly spoiler territory. That said, the stories also differ, most notably in their setting (Cross Ange involves mechs, while Yona is set in a fantasy realm inspired by ancient Korea and China), their story type (Cross Ange gives more attention to action and uses its story beats in emotionally gratifying ways, while Yona gives more attention to its characters and features more morally ambiguous setting details), and their intended audience (Cross Ange seems very much oriented toward a male audience, particularly given its sexual fanservice elements involving its nearly all-female cast, while Yona's cast of prettyboys shows its orientation toward a female audience). Also, Cross Ange is a complete story, whereas Yona could definitely use a second season -- but at least its 3 OVA episodes add a good deal of story content, so make sure to check those out after you've finished the main series.