Heat 2-inches vegetable oil in a large, wide, heavy saucepan until it registers 370 degrees F. Whisk together the flour, baking powder, zest, and salt in a bowl. Whisk together the ricotta cheese, eggs, granulated sugar, and vanilla in another bowl, then whisk into the flour mixture. Working in batches, gently drop in tablespoons of batter and fry, turning occasionally, until deep golden, about 3 minutes per batch. Transfer with a slotted spoon to paper towels to drain. Dust generously with confectioners' sugar, garnish with lemon zest and serve with Quick Berry Jam.
Combine the berries and 1/2 cup of the sugar in a bowl and coarsely mash with a potato masher. Let the berries sit at room temperature for 15 minutes to allow the berries to release some of their juice. Taste for desired sweetness and add remaining sugar if necessary. Transfer berries to a medium saucepan, add lemon juice and cook until thickened, about 5 minutes. Transfer to a bowl, cover and refrigerate until chilled or serve immediately: transfer to a bowl and set the bowl over an ice bath, stirring until jam is cooled.