Its not complicated though, The Federal Reserve a corporation run by a board of directors, those people decide how much money to make and who to give it to (mostly themselves/other bankers).
The share holders of the Federal Reserve are ALL private "regional" banks, then the profit of the Federal Reserve is shared with its shareholders. The two largest shareholders (owners) of the Federal Reserve, together with over 50% ownership is Citi and Chase. So Citi and Chase own the federal reserve.
This is simply false, though it's an exceedingly common false belief:
The Federal Reserve System is not "owned" by anyone. The Federal Reserve was created in 1913 by the Federal Reserve Act to serve as the nation's central bank. The Board of Governors in Washington, D.C., is an agency of the federal government and reports to and is directly accountable to the Congress.
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Some observers mistakenly consider the Federal Reserve to be a private entity because the Reserve Banks are organized similarly to private corporations. For instance, each of the 12 Reserve Banks operates within its own particular geographic area, or District, of the United States, and each is separately incorporated and has its own board of directors. Commercial banks that are members of the Federal Reserve System hold stock in their District's Reserve Bank. However, owning Reserve Bank stock is quite different from owning stock in a private company. The Reserve Banks are not operated for profit, and ownership of a certain amount of stock is, by law, a condition of membership in the System. In fact, the Reserve Banks are required by law to transfer net earnings to the U.S. Treasury, after providing for all necessary expenses of the Reserve Banks, legally required dividend payments, and maintaining a limited balance in a surplus fund.
Note the mention of "legally required dividend payments" in the 2nd 'graph above. Those are in fact accrued to the member banks, and amount to 6% of the stock price (itself, if I'm reading correctly, 6% of the total asset value) of each regional Federal Reserve Bank.
Strictly speaking this is not profit, though the dividends are only paid when the Fed itself has positive operating returns (which is almost always). But it is, yes, a benefit which accrues to member banks.
The operating profits however are paid to the U.S. Treasury.