Heat the olive oil in a saute pan over medium-high heat. Add the onions and saute till translucent and slightly browned, about 5 minutes. Let cool.
Place cornmeal, flour, salt, baking powder, and pepper in a large bowl and whisk together to blend. Make a well in the center of the flour mixture and add the eggs and water.
Blend sparingly till dry ingredients are just moistened. Batter will be thick. Fold in the cooled onion mixture and okra.
In a heavy skillet, pour oil to a depth of 1 inch and heat to 350 degrees F. Line a baking sheet with parchment paper. Scoop 2 heaping tablespoons of batter per fritter onto the lined baking sheet and flatten each slightly with the back of the spoon.
Using a spatula, lift each patty and slide each into the hot oil. Cook a few at a time, being careful not to overcrowd the pan. Fry until golden brown on one side, approximately 2 minutes.
Carefully flip the fritter and continue to fry on the other side until golden brown, approximately 2 minutes. Remove from oil and drain on a rack.