Will this recipe for vegetable fritters freeze well?
You can freeze fritters like this after frying, but I'd recommend freezing the vegetables by themselves or freezing the cooked fritters, or simply shrinking the recipe.
Whether you refrigerate or freeze the cooked fritters, you'll want to re-fry the floppy fritters to get the crispy texture back, unless you're okay with floppy fritters (they're kind of good honestly, like cold pizza). This is convenient like any other freezer meal.
But your recipe is very simple. If you only want 1 fritter, just measure out 25g of each ingredient instead of 200g. If you want 2 fritters, measure out 100g.
Realistically, you will almost certainly have extra veg that you won't need for this recipe, so regardless of how many fritters you make, if this is a recipe you like, I'd recommend freezing the excess carrots and beets for use in the next batch.
I will point out that doing do will cause a lot of moisture to be released when the veg is thawed. So for that reason I specifically DO NOT recommend freezing the batter before frying it. The consistency will be very different once thawed and all that water's released.
One way to circumvent this (and probably reduce your cooking time) would be to salt all your shredded veg. The salt would draw moisture out as well, even is you just use a pinch. Let it sit in the salt for a bit, then wring it out in a kitchen towel and continue with your recipe. You could even save the salted juice to use as your binding liquid instead of water.