Wash the maties, dab dry and cut into small cubes. Peel onions and chop one finely. Wash and quarter the apple and cut out the core. Cut the apple into small pieces.
Mix the maties, diced onion, apple and capers. Mix lemon juice and 2 tablespoons of oil and season with salt, pepper and sugar. Wash the dill, dab dry and chop finely, except for a little for garnishing.
Add sauce and dill to the tartare. Mix everything and let it stand for about 30 minutes. In the meantime peel and wash the potatoes. Grate potatoes and remaining onion roughly. Add egg and flour and mix.
Season with salt and pepper. Heat the remaining oil in a frying pan. Add approx. 1 tablespoon of potato mixture to each pan and flatten it slightly. Fry on medium heat for 3-4 minutes on each side until golden brown.
Arrange the Rösti with Matjestatar on plates and serve to taste with lemon wedges, remaining dill and possibly garnished with apple slices.