Place the grated zucchini in a bowl and mix in a pinch of salt. Set aside.
Peel, rinse, and grate potatoes. Place grated potatoes in another bowl and rinse with water to get rid of some of the starch. Drain and squeeze out excess water.
Take the grated zucchini and squeeze out excess water. Mix in grated potatoes and garbanzo bean flour. Give the grated vegetables another big squeeze to drain out excess water. Mix in the eggs, chives, turmeric, about another teaspoon or two of salt, and pepper.
Heat 2 tablespoons of olive oil on a pan or skillet over medium-high heat. Scoop out 1/3 cup of the vegetable mixture and place it on the hot pan. Use a spoon to flatten out the mixture to rounds that are about 1/3 to 1/2 inch thick. I cooked 4 fritters at a time. Pan fry each side for 3 to 4 minutes, or until the edges are golden brown. Plate the cooked fritters. Pour another 2 tablespoons of oil into the pan, and continue cooking the rest of the fritters. Add more oil as needed.
Serve fritters with tzatziki sauce if you want. Best served immediately.