Place the new potatoes into a saucepan, cover with water and add a pinch of salt, a knob of the butter and half of the mint. Bring to the boil and cook the potatoes for 4-5 minutes, or until tender. Drain.
Mix the lemon zest, juice, sugar and capers together in a large bowl. Stir in the potatoes and season, to taste, with salt and freshly ground black pepper. Add the remaining butter, reserving a knob of butter to fry the fish, and set aside.
Rub the dab fillets with the oil and with salt and freshly ground black pepper.
Heat the reserved butter in a frying pan and cook the fish for 2-3 minutes on each side, or until cooked through.
To serve, spoon the potatoes onto serving plates and top with the dab fillet.