This answer is limited to the USA.
As held by the 8th circuit in Kennedy C. Scott
v. Federal Reserve Bank of
Kansas City, et al.:
The Bank also does not constitute an federal agency based on any “proprietary
interest” the United States possesses. The Bank is considered a separate corporation
owned solely by commercial banks within its district, distinct from the Board of
Governors. See 12 U.S.C. §§ 282, 287, and 341. The United States does not own stock in the Bank. Id.; see also Lewis v. United States, 680 F.2d 1239, 1241 (9th Cir.
1982) (explaining the structure of Federal Reserve Banks).
According to the Federal Reserve itself:
Under the Federal Reserve Act, each of the twelve Reserve Banks is separately incorporated with its own board of directors. In each Reserve District, commercial banks that are members of the Federal Reserve System own the stock of their District's Reserve Bank and elect the majority of the Reserve Bank's board of directors; the remainder of the directors are appointed by the Federal Reserve Board.
According to the Federal Reserve Bank of Richmond (one of the twelve Federal Reserve Banks):
More than one-third of U.S. commercial banks are members of the Federal Reserve System. National banks must be members; state chartered banks may join by meeting certain requirements.
Each state member bank must hold capital stock in the Richmond Fed
So the 12 Federal Reserve Banks of the United States are owned by a large list of banks, not any one particular family.