Stir together squash and 1/4 teaspoon of the salt in a large wire-mesh strainer set over a large bowl. Let stand until squash has released water, about 15 minutes.
Discard liquid. Place squash in a kitchen towel, and squeeze to remove excess water. Add squash to a large dry bowl.
Add flour, Parmesan, and eggs to the bowl. Stir.
Heat 1 tbsp of the oil in a large nonstick frying pan on med. heat. Take two tbsp of the squash mixture, flatten it. Place it in the pan. Repeat this process until you can't fit anymore patties. Cook until crispy and golden brown. Should take about 2-3 minutes.
Flip and brown the other side. Another 2-3 minutes.
Place on plate with paper towels to absorb the grease.
Repeat the process until all of your mixture is gone.
Sprinkle the remaining salt (if desired) on the fritters. Top with the sour cream and green onions (if desired). Serve.
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