From Ohio History Central
Since the late 1700s, various states have claimed ownership of various stretches of the Ohio River. The principal reason was to garner wealth from the trade that occured on the river. In 1792, the federal government determined that Kentucky owned the Ohio River along its border with Ohio, Indiana, and Illinois. In essence, the boundary between Kentucky and these three future states would be the low point of the Ohio River's northernmost bank.
Both Indiana and Ohio have sought to claim the Ohio River, despite the federal government's declaration in 1792. In 1966, Ohio claimed that the Ohio River's course had fluctuated since 1792, so that the low point of the Ohio River's northernmost bank in 1792 actually would be near the south bank of the river today. Ohio asked the United States Supreme Court to give ownership of the river to Ohio or, at the bare minimum, to set the boundary between Kentucky and Ohio in the midpoint of the Ohio River. The Supreme Court ruled that Kentucky had legal ownership to the Ohio River.