Heat 1 Tbsp olive oil in a large skillet over medium heat. Put corn and zucchini in the skillet and season with salt and pepper. Cook for about 3 minutes, stirring often, until vegetables soften. Remove to a large bowl and let cool slightly. Wipe skillet out and set aside.
Once corn has cooled slightly, add scallions, eggs, cornmeal, flour, paprika, garlic powder, and feta to the bowl. Stir to combine.
Add remaining 2 Tbsp oil over to skillet over medium heat. Scoop out about ¼ cup of the corn mixture and form into a small patty with your hands. Place in skillet and cook for about 3 minutes, until bottom is getting crispy and turning golden. Flip and cook for another 2 minutes. You can cook several at a time.
Transfer to a plate covered with a paper towel and repeat until you've used all of the corn mixture. Add more oil to skillet if necessary.
Serve warm with crumbled feta cheese and scallions over them.