If you're using a wet vegetable like zucchini or squash as your main, you'll want to squeeze out the liquid. You can do this by wrapping the shredded vegetable in a cheese cloth or clean kitchen towel and wringing it out.
Combine vegetable, greens, onion, salt, and baking powder in a large bowl. Stir in ¼ cup flour and mix until flour is well incorporated into vegetables. Add in egg and mix. If mixture feels too wet, add in additional flour, 1 tablespoon at a time.
Heat a tablespoon of oil in a heavy bottomed skillet over medium high heat. Drop in 2-3 tablespoons of fritter batter and push down gently with a spatula. Fry until golden brown on one side, about 2 minutes. Flip and brown on remaining side. Repeat until all of batter is used up.