I'm suffering myself mainly from Asperger's, OCD and bipolar type 1 and I'm seeing a therapist, psychiatrist, on medication in real life and disability for life because I can't work because of these very serious mental health issues. I'd like an FL who's strong and who has either a physical or mental disability like I do or who goes through hardships or some ordeals in life, and who on top of that, is poor and ordinary, but always stays strong, sunny, happy-go-lucky and optimistic in life.  Like their life isn't all roses and sunshine at all. ML and SML are rich, powerful and cold, and arrogant. FL leads a simple and frugal life due to being dirt poor financially. Now, I've already seen all the "Meteor Garden" versions, "Boss and Me" and "Well-intended Love", as well as "1 Litre of Tears." Looking for something much like "Well-intended love" and "1 Litre of Tears" where FL overcomes many hardships in life including a terminal illness. Those are my favourite modern romances to feel connected to. I feel I can really relate to the FL in those dramas, because I'm a severely physically and mentally disabled person as well as financially very poor, but happy and sunny just like them. I love to enjoy and appreciate every moment in life just as they do in those dramas. Any country, any language but a modern drama please.

Some k-dramas that you may enjoy (not all of them will be a 100% fit, but perhaps they are close enough to what you are looking for). Also most of them feature FLs who have PTSD due to trauma:

  • The Light in your eyes
  • Healer
  • It's Okay, That's Love
  • Just Between Lovers
  • Always (movie) 
  • Forest
  • Devilish Joy
  • He is Psychometric
  • Kill me, Heal Me
  • Lie after Lie
  • Oh my Ghostess
  • Soul Mechanic
  • The Master's Sun
  • Thirty but Seventeen

the K2 - FL has PTSD and psychological problems, fears of people and lights

It's Okay to not be okay - SML is autist and it's big part of the story, how ML (his brother) takes care of him, their relationships, it's very good show. FL has her own psychological problems too

None of these are really what you're looking for, but it's the best I could come up with.

Yamato Nadeshiko Shichi Henge - I don’t think FL is actually mentally ill, but she’s definitely not “normal.” She’s severely antisocial, among other things. She definitely doesn’t go about life with a cheerful attitude, though. The drama is about her growth. ML isn’t rich, but I think SML might be? I don’t really remember their personalities that well. It has a very exaggerated style, but I thought it was charming.

Tatta Hitotsu no Koi - Female lead is in recovery from leukemia. I also think she has a pretty positive outlook on life. However, FL is rich, while ML is poor. ML also has a sick brother (cystic fibrosis I think). I’m not sure how I would describe ML’s personality. He feels like a real person, not a stock romantic lead.

My Holo Love - I think FL has prosopagnosia. But if I remember correctly, the plot is more focused on around the AI aspect than on her disorder. ML is either an AI or the programer who made the AI (I don’t remember that well).

Boku no Ita Jikan - ML is the one who is sick (ALS), but it definitely deals with themes like appreciating life through the hardships.

It's not a drama but a  kmovie,  "Josee,"  the first version is japanese but I don't remember the name. 

I dont know if this is what you are looking for but ... Mokomi: Kanojo Chotto Hendakedo There are some fantastical elements but it feels as if its all a metaphor for autism/asperger. Seeing things not as other people see them.