The Federal Reserve System has a number of facets, such as regulation, policy setting and research which are clearly 'owned' by the public just like any other agency.
The regional Banks are a hybrid. Their capital is supplied by the chartered commercial banks in the region who are required to buy stock in the Bank, so there is an element of private ownership, but all of the profits from the system go to the federal government and the member banks get a fixed dividend on their investment in their regional Bank.
The governance of the system is via a board nominated by the President and the regional member banks can also elect some board members of their local Bank.
Given that all of the profits from the system go to the public, it's essentially public ownership.
All of this is easily found information. Do you have an underlying question?
You really didn’t answer my question.
But here is another one for you.
Do you think it is wise to outsource one of the most important functions of Government (money creation) to a private entity?
The legitimate functions of the FR should be adsorbed by the Treasury Department.