Peel and cut potatoes into 1.5 cm sticks. Soak in cold water for at least 20 minutes.
Drain and dry the chips thoroughly. Heat oil to 135°C. Fry chips in batches for 6 to 8 minutes until pale and cooked through. Lift onto a wire rack.
Whisk flour, baking powder, salt, and paprika together. Pour in the ice-cold beer. Whisk just until combined (10 seconds) — lumps are fine. Rest in the fridge.
Mix all tartare ingredients in a bowl. Taste and adjust.
Heat oil to 190°C. Re-fry chips in batches for 2 to 3 minutes until deep gold and crisp. Salt immediately.
Dust each fish fillet in the extra flour. Dip in batter, let excess drip.
Fry fish two fillets at a time at 190°C for 4 to 5 minutes until deep gold.
Drain on a wire rack, not paper towel. Salt immediately.
Serve with chips, tartare, lemon wedges, and malt vinegar.