Heat a heavy bottomed saucepan, a third full of vegetable oil, until a breadcrumb sizzles in it. (CAUTION: hot oil can be dangerous! Do not leave unattended.)
Place the flour in a large bowl and beat in the egg and salt and freshly ground black pepper, to taste.
Add the carbonated water and whisk to create a batter the consistency of double cream.
Dredge the sole pieces in flour then dip pieces into the batter to coat.
Place in the hot oil and deep-fry for 2-3 minutes, until crisp and golden. Carefully remove using a slotted spoon and drain on kitchen towels.
To make the dip, mix the yoghurt with the chives and lime juice. Transfer to a serving bowl.
Serve the fish fingers on a plate with the dip and lime wedges alongside.