Heat four 1-cup jars and lids.
In a large pot, combine sugar, water or apple juice, and lemon juice. Bring to a boil over high heat, stirring to dissolve sugar. Add apple, orange, and raisins. Reduce heat and boil gently for 7 minutes.
Add blackberries, increase heat to high, and return to a boil. Boil hard, stirring constantly for 15–20 minutes, until mixture thickens. Remove from heat and test for set.
Skim and discard any foam. Fill hot jars, leaving 1/4-inch headspace. Top with lids. Process jars at a full rolling boil for 15 minutes.