So here are my recs:
My Mister- it's not really psychological in style of for example Hello Monster but it deals with problems and psychic of ordinary people facing hardships, the plot is well-written and I must say it's the objectively best drama I have watched
Kill Me Heal Me- if you haven't watched this you must!!! It's not only psychological but practically medical- ML has Dissociative identity disorder and FL is psychiatrist , it has great plot and twist and the best acting and chemistry between leads
The Smile Has Left Your Eyes- it's rather melodramatic, dark psychological drama, ML is one of the most interesting characters I saw in dramas, couple has great chemistry and plot is full of suspense
Cheese In the Trap- I really liked this one despite being unusal and underrated, ML has dark, mysterious character, plot is interesting with twist and suspense and actors are good in their roles