Soak cod in cold water to rehydrate it and remove excess salt, 8 hours to overnight.
Remove bones and skin from fish. Flake and shred fish into small pieces; set aside.
Sift flour, pepper, and baking powder into a large bowl. Add tomatoes, green onions, and flaked cod. Pour in 1/2 cup water; stir until well blended.
Heat 1/4 inch of oil in a large, heavy skillet over medium heat.
Drop rounded spoonfuls of batter into the skillet; fry in hot oil until golden brown and crisp, about 5 minutes per side. Drain on paper towels and serve hot.