Simmer the apple cider until reduced to about 2 tablespoons and syrupy, 8 to 10 minutes. Cool.
Parboil the sausages 5 minutes, drain, and pat completely dry.
Whisk the yolk, mustard, garlic, and cooled cider reduction. Add oil a teaspoon at a time until thickened and pale, then in a slow stream. Whisk in vinegar and salt; refrigerate.
Heat the oil in a heavy pot to 350°F, checked with a thermometer.
Whisk the flour, baking powder, smoked paprika, salt, and pepper, then whisk in the sparkling water just until combined.
Dust each sausage in the reserved flour, dip in the batter, and let excess drip off.
Fry two sausages at a time for 4 to 5 minutes until deep golden and crisp. Drain on a wire rack.
Rest 2 minutes, slice on the bias, and serve hot with the aioli.