Prepare the apples. Peel the apples and cut them into very small, fine pieces. The apples may also be shredded if preferred. Set aside until the batter is ready.
Combine the liquid ingredients. Place the eggs, ⅔ cup milk, and freshly squeezed lemon juice in a large mixing bowl. Beat until the ingredients are thoroughly blended.
Prepare the dry mixture. In a separate bowl, whisk together the all-purpose flour, baking powder, salt, granulated sugar, and ground cinnamon until evenly distributed.
Make the fritter batter. Gradually add the dry ingredients to the egg and milk mixture, stirring only until the two mixtures are combined. Gently fold in the prepared apples. Do not overmix; a slightly lumpy batter helps the fritters remain light and tender.
Heat the frying oil. Pour several inches of vegetable or canola oil into a deep, heavy pot. Heat the oil to 350°F (175°C).
Fry the fritters. Carefully lower generous tablespoonfuls of batter into the hot oil. If the batter forms compact, round portions, spread each one slightly. Cook only a few fritters at a time so the pot is not overcrowded and the oil maintains its temperature.
Brown both sides. Fry the apple fritters for approximately 3 minutes per side, or until they develop an even golden-brown color.
Drain and cool. Lift the cooked fritters from the oil with a slotted spoon and transfer them to a wire cooling rack. Allow them to cool slightly while preparing the glaze.
Mix the vanilla glaze. Whisk the confectioners’ sugar, vanilla extract, and 3 to 4 tablespoons of milk together in a small bowl until smooth. The glaze should have a relatively thin consistency. Add additional confectioners’ sugar if it becomes too loose, or a small amount of extra milk if it is too thick.
Glaze the fritters. Dip the slightly cooled fritters into the vanilla glaze, then return them to the wire rack so the coating can set. Alternatively, brush the glaze generously over the tops.
Serve. Enjoy the apple fritters while fresh for the best texture and flavor.