That sounds somewhat similar to the plot of Rab Ne Bana Di Jodi. I don't think I've seen any east Asian dramas that are a close fit, but maybe try The Eternal Love. The FL is from modern times, but her soul travels to another world that is similar to ancient China, and shares the body of a noblewoman who looks just like her. The noblewoman is in love with one prince, but is forced to marry another. The prince she marries is aware of the noblewoman's feelings for his brother and isn't interested in her, but after the FL takes over her body he starts to fall for her. The FL never likes the other prince, but she is focused on trying to get home for a while, and sometimes the noblewoman regains control of her body and does things that makes it seem like the FL has feelings for the other prince.
