Preheat oven to 350 degrees. Place tortillas on a baking sheet and top each with a tablespoon of jam, spreading it almost to the edge. Bake until tortilla is crisp, about 10 minutes. Remove and cool to room temperature.
Spoon 1/4 cup of ricotta over each tortilla, spreading it almost to the edge. Divide the berries among the tortillas, making alternating rows of raspberries, blackberries, strawberries, and blueberries. Brush tops with remaining jam. Serve immediately, cutting into wedges like a pizza.