In a large mixing bowl, combine shredded butternut squash, eggs, minced sage, salt, and pepper. Fold in flour and add more if needed in order to hold fritters together.
Add olive oil to a large skillet over medium heat, and heat until the oil sizzles when a drop of water is added. Drop 1/4 cup of the mixture at a time, making sure to keep the fritters at least 1-inch apart.
Cook about 2 minutes on each side, or until they are cooked through and golden brown.
When cooked, transfer them to a paper towel to absorb the excess oil. Repeat the procedure with the remaining mixture.