In a medium bowl, gently whisk the yogurt, egg, salt, sugar, and baking soda. Continue whisking, gradually adding the flour. Mix until you get a smooth and thick batter. Cover the bowl with plastic wrap and let the batter rest for 15 minutes.
Preheat 1/4 cup of the oil on a large frying pan until the oil is hot and shimmering. Drop a small scoop (about three tablespoons) of the batter into the hot frying pan and top with the apple slice. Reduce the heat to medium-low. Repeat the same steps with the remaining batter, but don't overcrowd the pan.
Cook the blinis until the bottom is crispy and golden brown and the top is not runny anymore. It will take a couple of minutes. Then flip each blini on the other side and fry for 2 to 3 more minutes, or until the apple becomes soft and caramelized. Transfer to a platter lined with a paper towel to absorb the excess oil. Sprinkle with cinnamon.