Most of the rhetoric about the Federal Reserve being private originally comes from the John Birch Society and other right-wing populist groups.
There are two main conspiracist variants:
secular: secret banking elites own the Fed to suck money out of the middle class. See: G. Edward Griffin, The Creature from Jekyll Island.
antisemitic: same as above but it is Jewish bankers controlled by the Rothschilds. See: Eustace Mullins, Secrets of the Federal Reserve.
Search the web on these two titles and open Pandora's box.
-Chip Berlet