  We construct a family of fermionic star products generalising the fermionic
Moyal product. The parameter space contains the polarisations necessary to
define a quantum Hilbert space. We find a star product of fermionic functions
on sections of the pre-quantum line bundle and show that the star product of
any function on a quantum state remain a quantum state. Associativity implies a
representation of the fermionic star product algebra on the quantum Hilbert
space. The star product is compatible with both the flat connection on the
bundle of fermionic functions and the projectively flat connection on the
bundle of Hilbert spaces over the space of polarisations.
