Xie Wang Zhui Qi

Both our female leads, who belong to the present time, are mysteriously taken back in time to ancient China. There, not only do they have to understand her mysterious teleportation, but also adapt into the bodies of girls who actually lived during that time period. And unlike the owners of those bodies, our MCs are sharp and lively, and do not hesitate to put men in their places when they try to control them. Both these girls are also paired with tsun leads, who could very well be each other's twin. 

I'll try to keep the similarities between these shows as brief as possible: 1. Both have 'strong' female leads with quirky personalities, and yet, both need to be saved by the male MCs in their lives. 2. Both have a brown haired cutie who's loyal to the prince 3. Both the female MCs have a handmaiden who's loyal to them 4. You get to see a lot of arbitrary magical powers, with little to no explanation about them. 5. Both girls are mistreated by their fathers bc of their past. 6. Both male MCs have a tragic past, which is supposed to be an excuse for their trash behaviour towards their female love interests. 7. Both girls feel little to no emotions towards the male MC, and can easily put him in his place (be it through words or through physical fights), but both girls also blush easily in his presence, because plot convenience. read more 

I know that the girl main character in this anime isn't the same as the main character in Fushigi Yuugi because the main girl character in Xie Wang Zhui Qi is a assassin But they do have a lot of similarity. The main girl character in this two anime across world and end up in a world which is traditional and has magic. The boy main character in this two anime is really strong too. And this two anime even has a king enemy who doesn't like the main boy character clan, he is really strong . 

Strong female leads.