Make the dough: Pulse the flour, granulated sugar, baking powder and salt in a food processor. Add the butter and shortening and pulse until the mixture looks like coarse meal. Drizzle in 6 tablespoons ice water and pulse until the dough starts coming together.
Turn the dough out onto a piece of plastic wrap and lightly knead to bring together. Form into a disk, wrap in the plastic wrap and refrigerate until firm, about 1 hour.
Meanwhile, make the filling: Combine the cherries, granulated sugar, cinnamon and salt in a medium saucepan over medium heat. Cook, stirring, until the cherries are juicy and the sugar dissolves, about 5 minutes. Bring to a simmer and cook, stirring, 5 more minutes. Spoon about 2 tablespoons of the juice into a small bowl; stir in the cornstarch until dissolved. Pour the cornstarch mixture into the saucepan and continue to simmer, stirring, until very thick, 6 to 8 more minutes. Transfer to a bowl, stir in the lemon juice and let cool.
Divide the dough into 8 pieces and roll each into a ball. On a lightly floured work surface, roll out each ball into a 6 1/2-inch round, using as little flour as possible. Stack the rounds between pieces of parchment paper and refrigerate until firm, about 30 minutes.
Remove the dough from the refrigerator and let stand 5 minutes. Place 2 tablespoons cherry filling in the center of each round, then fold in half to enclose and crimp the edges to seal.
Heat 1 inch of vegetable oil in a deep skillet until a deep-fry thermometer registers 360 degrees F. Fry the pies in 2 batches, turning once, until golden brown, about 3 minutes. Transfer to a rack to cool. Dust with confectioners' sugar.