HEAT a large non-stick frying pan over medium. Add oil, then onion and eggplant. Cook until onion is soft, 5 min. Add tomatoes, garlic, paprika and sugar. Use a potato masher to break up tomatoes. Reduce heat to medium-low. Simmer, covered, until saucy, about 15 min.
ADD fish fillets, then spoon sauce over fish. Simmer, covered, until a knife tip inserted in thickest part of fish and held for 10 sec feels warm, 6 to 8 min. Sprinkle with capers and parsley.