looking for dramas that have a missing child and the spend years looking them

can you please help me

ok  thank you

Beautiful Gong Shim

Missing you/ I miss you could fit this as well.

Boy and Girl get kidnapped (high school age) and the boy spends his adult life searching for her after they get seperated.

Kill me heal me

Hello Monster (aka I Remember You). 

Here are a few I know with lost/estranged family. Some of these are parents or grandparents who are looking/find kids/grandchildren after years.

Jang Bori Is Here 

Mei-chan no Shitsuji

Mussaya

My Girl

Prince Of Wolf

Romantic Princess

Rooftop Prince

Stars Falling From The Sky

Beautiful Gong Shim