To make the mayonnaise, in a medium bowl whisk together the mayonnaise, lemon juice, parsley, horseradish, salt, pepper and all but a pinch of the lemon zest. Spoon into a small ramekin and garnish with additional parsley and the remaining zest. Set aside.
To make the fritters, in a large skillet over medium-high, heat 2 tablespoons of the oil. Add the onions and saute until softened and lightly browned, about 8 minutes. Add the garlic and cook for 1 minute. Transfer the onion mixture to a bowl to cool slightly.
Wipe the skillet with a paper towel and set aside.
In a large bowl, use a fork to mix together the mashed potatoes and eggs. Stir in the quinoa, matzo meal, parsley, salt, pepper and the sauteed onion mixture.
Return the skillet to the burner over medium-high. Add the remaining 1/2 cup of oil and heat until very hot but not smoking.
One at a time, scoop the fritter mixture into balls about 2 tablespoons each. Place 4 or 5 balls in the skillet, then use a lightly oiled spatula to gently flatted them. Cook until golden brown and crisp on the bottom, about 2 minutes.
Flip the fritters and cook for an additional 2 minutes, then transfer to paper towels to drain. Repeat with remaining fritters. Serve the fritters with the mayonnaise.