Blitz or chop the Barramundi fillet until preferred patty texture, i.e. chunky or smooth. Add the oil, lemon, paprika, mustard and salt and mix well until combined. Divide the patty mix and roll to form 6 patties. Place in a container with a lid or cover with cling film and chill in fridge for 30 minutes.
Combine the tempura ingredients a large bowl to make a batter like wet paint (or your preferred consistency). Then dredge patties in extra flour, dip in batter and fry until golden brown.
To assemble, toast the brioche buns, then layer the lettuce, aioli and patties.