Grate the zucchini on the large holes of a box grater. Toss with 1 tsp salt in a colander set over a bowl and let it sit for 15 minutes to draw out the water.
Working in batches, squeeze the grated zucchini hard in a clean kitchen towel until barely any liquid drips out. This step matters, skip it and the batter turns thin and won't hold together in the pan.
In a mixing bowl, combine the squeezed zucchini, crumbled feta, eggs, flour, dill, mint, green onions, and black pepper. Mix until you get a thick, scoopable batter.
Heat 3 tbsp olive oil in a 12-inch nonstick skillet over medium heat until it shimmers.
Scoop about 2 tbsp of batter per fritter and drop into the hot oil, flattening slightly with the back of the spoon. Fry 4 to 5 at a time so you don't crowd the pan.
Cook for 3 to 4 minutes per side, until deep golden brown and set in the middle. Flip once with a slotted spatula.
Transfer cooked fritters to a paper towel-lined plate. Add more oil to the skillet between batches as needed and repeat with the remaining batter.
Serve warm or at room temperature, with tzatziki and a lemon wedge on the side.