Its ownership is unique, being unlike any other corporation in America. It's all right there in the Federal Reserve Act that created it. If I recall correctly...
From an Accounting standpoint, the capitol stock is owned by member banks for which they get paid 5% on the amount contributed annually. Each member bank gets one vote in electing the board of directors for the district bank, no matter how large or small the bank is.
But most of the profits, those in excess of the 5% paid on the member bank's capitol stock gets paid every year to the US Treasury. The payments get announced every year.
From a control standpoint, each Federal Reserve District bank is controlled by a board of governors that is must be 1/3 from the banking industry elected by member banks, 1/3 from businesses served in the district elected by member banks, and 1/3 presidential appointees.
The Board of Governors are appointed by the President in staggered 14 year terms.
And if you want to know what types of securities are owned by the FED, go to page 5 of the 2020 combined report and look at the assets. A link to the audited financial statements was previously posted by me in this thread.