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Place the zucchini in a clean dish towel and squeeze out as much water as you can.
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In a bowl, combine the zucchini, flour, 2 tablespoons of the chives, eggs, 1-1/2 teaspoons salt, and pepper to taste. Stir to combine.
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Line a baking sheet with paper towels.
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In a large skillet over medium-high heat, heat the oil until shimmering but not smoking.
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Working in batches to not overcrowd the pan, using clean, damp hands, scoop up about 2 teaspoons of batter, shape it into a 1-1/2-inch-wide disk, carefully place in the hot oil, and fry until golden brown on the bottom, 2 to 5 minutes, depending on the heat. Flip and cook the other side until golden, another 2 to 4 minutes.
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Transfer to the prepared baking sheet to drain. Keep warm.
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To serve, arrange the fritters on a platter. Top each with a folded piece of smoked salmon, ¼ teaspoon of sour cream, and a sprinkle of the remaining chives and the lemon zest.