Preheat the oven to 375°F (190°C).
Place the salmon fillets on a baking sheet lined with parchment paper and drizzle with teriyaki sauce.
Bake the salmon for about 15-20 minutes, or until it flakes easily with a fork.
While the salmon is baking, prepare the pineapple by dicing it into small cubes.
Once baked, remove the salmon from the oven and let it cool for a few minutes, then flake it into large pieces.
In a large bowl, combine the flaked salmon, diced pineapple, and half of the shredded cheese.
Heat one tablespoon of vegetable oil in a large skillet over medium heat.
Place one tortilla in the heated skillet, then spoon a generous portion of the salmon and pineapple mixture on half of the tortilla, topping it with some more cheese.
Fold the tortilla over and cook for 2-3 minutes until golden brown, then flip and cook for an additional 2-3 minutes on the other side.
Remove the quesadilla from the skillet and repeat the process with the remaining ingredients, adding more oil if necessary.
Allow the quesadillas to cool for a moment before cutting them into wedges and garnishing with chopped green onions.