Simmer apples, water, sugar, lemon juice, cinnamon, and salt in a medium saucepan over medium heat.
Cover and cook, stirring occasionally, until apples are very tender, 15–20 minutes. Mash to chunky or smooth. Keep warm.
Shred potatoes and grate onion. Wrap in a clean towel and wring out as much liquid as possible.
Whisk eggs in a large bowl. Add potatoes, onion, matzo meal, baking powder, salt, and pepper. Mix until just combined.
Heat a large skillet over medium to medium-high. Add oil to a thin layer, about 1/4 inch deep.
Scoop heaping tablespoons of batter into the pan. Flatten gently. Fry until deep golden, 3–4 minutes per side.
Transfer latkes to a rack or paper towels. Sprinkle with a pinch of salt. Repeat with remaining batter, adding oil as needed.
Serve latkes hot with warm or chilled applesauce. Add sour cream if you like.