Combine the gin, jam and some ice cubes in a cocktail shaker. Shake for 15 seconds, then strain into a coupe glass. Top with a splash of sparkling water. Serve immediately.
Combine the peaches, sugar and lemon juice in a nonreactive medium saucepan and bring to a boil over high heat, stirring occasionally. Reduce the heat and simmer, mashing the peaches occasionally with a potato masher, until the mixture thickens and sticks to a spoon, about 20 minutes.
Remove the saucepan from the heat and stir in the raspberries. Let cool to room temperature, stirring occasionally. Transfer the jam to a nonreactive container with a lid and refrigerate until ready to use. The jam will keep in the refrigerator for up to 1 week.