The American Civil War was a war fought between the Union, North, and the Confederacy, South.
There are only four known demigods involved in this war, although numerous children of Athena and Ares probably fought. Joshua Lawrence Chamberlain, General Sherman, sons of Ares, Harriet Tubman a daughter of Athena, and Thomas Jefferson Jr, a child of Tyr. Numerous soldiers from both sides made it to Valhalla.
Clarisse helps Percy, Tyson, and Annabeth defeat the Hydra with a Confederate Ironclad warship. The book mentions that in every war, the losing side has to give Ares a small fraction of their dead soldiers, giving Ares control over them.
The Roman and Greek demigods had a giant battle that lasted three days in Camp Half-Blood's woods around the time of the American Civil War. The loss of life was so great, the gods were forced to separate them and bind the Mist as tightly as possible so the two sides would forget each other. Chiron told the other campers about Bunker 9, a secret war base used when the Roman and Greek Demigods were fighting each other around the time of the American Civil War when he and the other campers (Hephaestus, Athena, Hypnos, etc.) were shown to the bunker by Leo Valdez who opened it after the Quest to save Hera with Jason Grace and Piper McLean.
While talking about a map to lead them to the Mark of Athena, Jason mentioned that it could be in one of the first ironclad submarines ever created during the Civil War. The quest group of the Prophecy of Seven discusses the Civil War, and Jason remarks that many (although not all) Roman demigods fought for the Confederacy. It is implied, although not stated, that most Greek demigods fought for the Union. Hazel takes great offense to this as her grandmother was a slave. It is also said that the many Romans fought for the south as the Confederates were the first to design ironclad ships, but Jason says that not all Romans fought for the South, just like how not all Greeks fought for the North.