Combine the dry ingredients. Whisk the flour, baking powder, salt, and sugar thoroughly in a large mixing bowl so the leavener is evenly distributed.
Mix egg and yogurt. Briefly beat the egg in a separate bowl, then stir in the yogurt until smooth.
Make a sticky dough. Add the yogurt mixture to the dry ingredients. Stir with a sturdy spoon or spatula only until no dry flour remains. Do not knead. The dough should be thick, soft, and distinctly sticky, holding a mound on a spoon rather than running like pancake batter.
Rest for 20 minutes. Cover and leave at room temperature for 20 minutes. This is a short dough rest, not a yeast rise. Do not prepare it hours ahead or beat it vigorously after resting.
Reserve cold oil. Before heating the frying oil, set a little of it aside in a small dish for coating the portioning spoons. Keep this dish away from the hot pot.
Prepare the frying pot. Pour the remaining oil into a small deep heavy pot, aiming for about 1¼–1½ inches (3–4 cm) depth. Leave ample headroom and never fill more than one-third of the pot. The listed oil quantity is approximate; pot dimensions determine the amount needed. Do not pour a scaled 2x or 3x supply into the same small pot.
Heat and prepare to drain. During the final 10 minutes of the dough rest, heat the oil slowly to 340–350°F (170–175°C). Monitor with a deep-fry thermometer. Prepare a plate or rack lined with paper towels.
Oil the spoons. Lightly coat two tablespoons with the reserved cold oil. Do not wet them with water: water droplets can make hot oil spit. Leave the rested dough otherwise undisturbed.
Drop small portions. Scoop a heaping spoonful of dough, about 35–40 g (1¼–1⅖ oz). Use the second spoon to ease it into the oil from close above the surface, keeping your hands clear. Add only 3–4 pieces at a time, with room to float and turn.
Fry the first side. Fry for about 2 minutes, until the underside is golden. Adjust the heat to keep the oil at about 330–350°F (165–175°C), avoiding both sluggish frying and rapid darkening.
Turn and finish. Turn gently with a slotted spoon and fry for another 2–3 minutes, until golden all over. Time is a guide; the interior must cook through before the crust becomes dark.
Check the first fritter. Remove one, allow it to cool briefly, and break it open. The center should be soft and airy, with no wet or doughy core. If the outside browns before the center cooks, make the next portions smaller and reduce excessive heat within the stated frying range.
Drain without piling. Lift out the cooked fritters with a slotted spoon and let excess oil drain, then transfer to the prepared paper towels. Avoid immediately packing or tightly covering the hot fritters.
Recover heat and repeat. Before adding another batch, let the oil return to about 340°F (170°C). Continue with the remaining dough in small batches, lightly oiling the spoons again as needed. Expect about four batches for the standard quantity when frying four at a time; larger batches of dough take longer.
Serve warm. Let stand for 2–3 minutes before eating. Serve warm with plain yogurt, cheese, commercially prepared kajmak, ajvar, honey, or jam as desired. These accompaniments are not included in the recipe quantities or calorie estimate.
Cool and handle the oil. Turn off the heat and let the frying oil cool completely in a safe place before filtering for suitable reuse or disposing of it according to local guidance. Do not pour oil down the drain.