Place zucchini in a colander set in the sink, and toss with 1 teaspoon salt; let drain 10 minutes. Press out as much liquid as possible.⏱ 10 min
Whisk egg in a large bowl; mix in zucchini, scallions, flour, and 1/4 teaspoon pepper until combined.
Heat oil in a large skillet over medium heat. Cook fritters in two batches: Drop six mounds of batter (2 tablespoons each) into skillet; flatten slightly. Cook, turning once, until browned, 4 to 6 minutes. Transfer to a paper-towel-lined plate; sprinkle with salt. Repeat with remaining batter. Serve immediately, with sour cream.⏱ 6 min