How to install OS X 10.9 on a new Mac mini loaded with OS X 10.11
You probably can not do this. The older versions of the Apple OS X operating systems are not capable of running on hardware yet to be designed. For this to work, Apple would have to have released an updated version of OS X 10.9, which they have not done. Therefore, OS X 10.9 will not be able to recognize your newer machine's hardware.  

PS: Apple has a support article for this as well, see Use the version of OS X that came with your Mac, or a compatible newer version.