"I care not what puppet is placed upon the throne of England to rule the Empire on which the sun never sets. The man who controls Britain's money supply controls the British Empire, and I control the British money supply."
There appears to be no primary source for this quote. It also makes no sense. At the time, there was no Rothschild sitting on the board of the Bank of England. BoE appeared to have borrowed money from the Rothschilds at some point, but this does not give the Rothschilds control of the money supply any more than I am in control of the US monetary policy because I owe a few treasury bonds.
Finally, as an economic matter, even if the Rothschilds owned 100% of BoE's debt, that would make them slaves to the BoE rather than the other way around.
There's no primary source. Moreover, this quote appears frequently in anti-Semitic agenda-driven sources as is easily documented by searching in Google Books.