Heat olive oil in a skillet over medium heat. Stir in onion; cook and stir until onions begin to turn translucent, 6 to 7 minutes.
Cook and stir in garlic until fragrant, about 30 seconds. Add capers and caper juice; stir to combine.
Stir in tomatoes, olives, jalapeno pepper, . Cook and stir until jalapeno pepper softens and tomatoes begin to collapse, about 3 minutes. Remove from heat; stir in oregano.
Drizzle 1 teaspoon olive oil into a small baking dish. Sprinkle in 1 tablespoon of the tomato-olive mixture. Top with 1 snapper fillet, salt, black pepper, and cayenne pepper. Top with more filling and juice from 1 lime. Repeat with remaining snapper fillet, seasoning, and lime juice in a second baking dish.
Bake in the preheated oven until fish is flaky and no longer translucent, 15 to 20 minutes.