Complex sentence: The 3rd Infantry was under the command of General Andrew Jackson during and after the war; a family story exists that Arbuckle served on Jackson's staff during the Battle of New Orleans in 1815, but no evidence has been found for this claim.
Split into simpler sentences: The 3rd Infantry was under the command of General Andrew Jackson during and after the war. A family story exists that Arbuckle served on Jackson's staff during the Battle of New Orleans in 1815, but no evidence has been found for this claim.