Cut the 1/2 lime into two wedges. Spear the mango slices on a cocktail skewer and place on a small plate. Squeeze the juice of 1 lime wedge over the mango slices.
Combine the chili powder, salt and sugar in a small bowl. Sprinkle the mixture on the skewered mango.
Fill a cocktail shaker with ice. Add the mango juice, apple juice and the juice of the remaining lime wedge. Shake well, then strain into a 10- to 12-ounce glass filled with ice. Top with the orange seltzer and garnish with the skewered mango and a sprig of rosemary before serving.