Preferably a serious drama, melodramatic or thrillers ( with or without romance)

 Where the male lead is very rich and cold hearted 

I was gonna say her private life but its not serious and more of a rom-com

Secret love (With Ji Sung and Hwang Jeung Eum)

boys over flowers comes to mind, but the korean version is kinda cringe now (it's originally japanese but i havent seen that)

the chinese version (meteor garden) and the thai version (f4 thailand) are much better, i think you'll enjoy those more. The chinese and korean ones are more of a rom-com and f4 thailand is a little darker and more serious.