Line a baking sheet with aluminum foil, then place a 4 1/2 by 8-inch flan form in the center of the foil.
In a 2-quart heavy-bottomed saucepan over medium heat, heat the raspberries until they begin to release their juice (about 5 minutes), stirring constantly.
Remove the pan from the heat and pour the raspberries into a fine-mesh strainer set over a bowl.
With a wooden spoon or heatproof spatula, press through as much of the raspberry juice as possible.
This should yield 2/3 cup raspberry juice.
In a small mixing bowl, dissolve the gelatin in the cold water.
In a 2-quart heavy-bottomed saucepan over medium heat, combine the raspberry juice, 1/2 cup of the sugar, and the corn syrup, and stir the mixture with a wooden spoon to dissolve the sugar.
Add the dissolved gelatin and stir constantly for about 5 minutes.
Remove the pan from the heat and immediately turn the mixture into the prepared flan form.
Let the candy set up completely at room temperature (2 to 3 hours).
With the blade of a large chefs knife, loosen and remove the flan form.
Cut the candy into eight 1-inch strips, then cut each strip into 4 pieces, forming 1-inch squares.
Place the remaining 1/2 cup sugar in a round cake pan, roll each square in the sugar to coat it completely, then place each square in a paper candy cup.
Between layers of waxed paper in a tightly covered container, the jellies will keep for 1 week at room temperature or 2 weeks in the refrigerator.
Substitute blackberries, strawberries, or blueberries for the raspberries.
Substitute 2/3 cup freshly squeezed lemon or orange juice for the raspberries.