Gently open each squash blossom, remove pistils or stamens, and wipe petals with a damp paper towel; set aside.
In a small bowl, combine ricotta cheese, Parmesan cheese, chopped chives, chopped parsley, 0.25 teaspoon salt, and a pinch of black pepper; mix until smooth.
Spoon about 1–2 teaspoons of the ricotta mixture into each blossom and gently twist the petal ends to enclose the filling.
In a medium bowl, whisk together flour, cornstarch, baking powder, 0.5 teaspoon salt, and 0.25 teaspoon black pepper; gradually pour in cold sparkling water and whisk until just combined (do not overmix).
Heat vegetable oil in a large heavy pot or Dutch oven over medium-high heat until it reaches 350–375°F (175–190°C).
Working in batches of 3–4, dip each filled blossom into the batter, let excess drip off, then carefully lower into the hot oil; fry 2–3 minutes per side until golden and crispy.
Transfer fritters to a wire rack set over paper towels to drain; immediately sprinkle with extra flaky sea salt and serve hot with lemon wedges.