Short answer: The treasury estimates 147.6 million ounces of gold are held at Fort Knox. The US government owns it. Both of those answers are controversial.
In 1933, the US government, on order of President Roosevelt, undertook to confiscate most of the gold owned by US citizens and exchange it for paper dollars within two weeks. Safety deposit boxes and vaults were sealed. Subsequently, US citizens were not allowed to own most forms of gold. The paper dollars were soon worth far less than the gold they were traded for. If that action is considered legal, the US government now owns the gold in Fort Knox. The vault was used to hold the treasure beginning in 1937. Before World War II, there were 649.6 million ounces of gold in Fort Knox. The treasury now estimates that only 147.6 million ounces remain. However, the gold has not been inventoried since the 1950's. Some believe there is far less gold in Fort Knox. In 1971, the US abandoned the last remnants of the gold standard. US dollars are now fiat currency, not backed by gold or any other commodity.