  The interaction vertex for a fermionic first order system of weights (1,0)
such as the twisted bc-system, the fermionic part of N=2 string field theory
and the auxiliary \eta\xi system of N=1 strings is formulated in the Moyal
basis. In this basis, the Neumann matrices are diagonal; as usual, the
eigenvectors are labeled by \kappa\in\R. Oscillators constructed from these
eigenvectors make up two Clifford algebras for each nonzero value of \kappa.
Using a generalization of the Moyal-Weyl map to the fermionic case, we classify
all projectors of the star-algebra which factorize into projectors for each
\kappa-subspace. At least for the case of squeezed states we recover the full
set of bosonic projectors with this property. Among the subclass of ghost
number-homogeneous squeezed state projectors, we find a single class of
BPZ-real states parametrized by one (nearly) arbitrary function of \kappa. This
class is shown to contain the generalized butterfly states. Furthermore, we
elaborate on sufficient and necessary conditions which have to be fulfilled by
our projectors in order to constitute surface states. As a byproduct we find
that the full star product of N=2 string field theory translates into a
canonically normalized continuous tensor product of Moyal-Weyl products up to
an overall normalization. The divergent factors arising from the translation to
the continuous basis cancel between bosons and fermions in any even dimension.
