Start by preheating oil in your deep fryer to 180 degrees celsius. if you don't have a deep fryer you can use a pot with oil, to check the oil is at the correct temperature test by frying a piece of bread to golden brown in 20 seconds.
Make the tempura batter, by combining the two types of flour in a large mixing bowl. Using a fork mix in enough soda water to make a thick batter. Season with salt.
Julienne the potato and add to the tempura mix, add the chopped parsley and chopped capers. Mix through with a fork.
Dredge with flathead fillets in the spare flour before placing into the batter.
Completely cover the fillets in batter. Carefully transfer the fillets one at a time to the hot oil and fry for 5-7 minutes until golden brown and cooked through.
Season the battered fillets and serve with aioli and lemon cheeks.