Using the shredding grate on a food processor, shred the zucchini, carrot, and potatoes. Mix together with the garlic, eggs, and plenty of seasoning.
Heat oil in a skillet. Using a slotted spoon or spoon, scoop up the vegetable mixture squeezing out the liquid. Press each scoop of vegetables into a patty shape as you squeeze them. As you are frying, the vegetable mixture will release more liquid and you can drain it out as you go along.
Add vegetable patties to oil and fry until golden on each side, flipping in between. Drain on a paper-towel lined plate.
Notes
Keep in mind that these won’t crisp up like latkes made from starchy potatoes so you don't want to make them too big or they will fall apart.