There is no mention of a "Battle of Jefferson" in William Faulkner's short story "A Rose for Emily." The story focuses on the life and death of Miss Emily Grierson, a woman who remains a recluse in the town of Jefferson, Mississippi, after the Civil War.
The story explores themes of isolation, tradition, and the decay of the Old South, but it does not reference any specific battles or historical events other than the Civil War itself.