The quesadilla originated in Mexico, which is indeed near the Caribbean, but is generally not considered part of the same culinary culture. My Dirty Rice was questioned because it's not technically from an island nation, too.I have not a clue from where quesadillas originated but this is one.
Stew Peas (Jamaican) which sounds delicious (it contains Scotch Bonnet which is another Caribbean 'S')
The stew is made using red beans, meat and is cooked an aromatic coconut milk broth with Jamaican spices and spinners (dumplings)
I presume that is not your image, MG.
I presumed that it wasn't because it's a very long way from your standard.