Prepare the batter: Mix the corn, eggs, cornmeal, flour, scallions, Parmesan, cilantro, lime juice, zest, salt, pepper, and smoked paprika in a large bowl. Chill the mixture for at least 10 minutes, longer is fine. I often make it earlier in the day, cover, and refrigerate for several hours. (Helpful hint: For added speed later, you may portion the batter into patties now and refrigerate on a parchment-line pan.)
For more evenly sized fritters: While you can drop the batter straight into the pan, I like to portion it out using a large ice cream scoop or greased ⅓ or scant ½ cup measure. Note that the batter will not fully stick together until it is cooked.
Cook the fritters: Heat 1 tablespoon of oil in a large skillet over medium heat. When hot, scoop the batter into the pan, spreading it lightly into thick but flat circles. I also nudge the edges in with a spatula as needed. Cook until golden brown on both sides, about 4 minutes per side. Remove to a plate. If your skillet wasn’t big enough to cook all the batter at once, add another teaspoon or two of oil and repeat with remaining batter.
Serve: Enjoy with the Smoked Paprika Aioli, as is, or with sauce of choice. Leftovers will keep for up to 5 days and may be gently reheated.