Drama with a relationship like tom and jerry?

Tom and Jerry? Perhaps you could explain in more detail what you are looking for?

I assume it's where the ML and FL have a stormy time during initial phase of the relationship, funny and cute.

• Childhood Frenemies - with bickering, teasing and fights:
  • Lovely Us
  • Reply 1994 (Kor)
  • Fight My Way (Kor)
  • Neung Nai Suang (Thai)
  • Adult Trainie - Story 3 / Episode 5 (?) (Kor)
  • Hello again (Twn)
  • Skate Into Love 
• The rivals - competition against each other
  • Divorce Lawyers 
  • All About Romance (Kor)
• The Enemies - clashing personalities and with power imbalance
  • Boys over flowers - all versions
  • Something about 1% (Kor)
  • Greatest Love (Kor)
  • King 2 Hearts (Kor)
  • Smile You (Kor)
• With Misunderstanding - couple with a past or exes
  • Discovery of Love (Kor)
  • Go Back couple (Kor)
  • Lets Eat 2 (Kor)
  • Our Beloved Summer (Kor)

I second Mr Bad and Love Between Fairy & Devil

I'll add Till the End of the Moon (2023), Flight to You (2022) and Never Give Up (2023)