Hong Gil Dong is about a Robin Hood type hero. It is set in Joseon. The credits identify the King as Gwanghae, who reigned from but events in the series take place 20 years into his reign, and events don't match up with history.
Watch Someone Special Movie. A struggling for love, Baseball players discovers he has terminal illness and meets a girl who has had a crush on him since times immemorial. The twists and turns of events bring them together.