Bring berries, Apple Balsamic and sugar to a boil in a medium saucepan over medium heat. Remove from heat.
Steep for 30 minutes for berries to release their juices. Strain through a fine-mesh sieve into a glass jar, pressing solids to extract as much liquid as possible. Cover; chill until cold. This concentrate can be made up to 3 days ahead.
When ready to serve, fill a 12 oz. glass with ice; add 2 T. of concentrate and top with club soda. Stir to blend.
1 pint raspberries, blackberries or blueberries, fresh or frozen, thawed