First, never use too high voltages on GPIO pins of an Arduino. if you want to know, search for 'absolute maximum current' or 'absolute maximum voltage'. Probably any pin of an Arduino is about 5 V (plus some headroom).
So since your fan will use more voltage high likely, you are not lost, in contrary, you should use a separate power source (giving the voltage you need for the fan), and use either a relay, or a transistor or MosFet. Than you can program it with a 5 volts pin and control a much higher voltage device (your fan).
Do not send high voltages/currents through breadboards and jumper wires neither. Use separate wiring, and you can check tables using AWG (thickness of wires) to see how much current they can support. Note that I say current, not voltage. The voltage will drop depending on the length of the wire and the size, so calculate that you have enough voltage at the end of the wire.
Also for safety, do not forget a fuse, and remember that the external power source and all wires have the same voltage as the fan, which may kill you if you touch them.