  We here propose a 5-dimensional {\bf Abelian gauge} model based on the mixing
between a $U(1)$ potential and an Abelian 3-form field by means of a
topological mass term. An extended covariant derivative is introduced to
minimally couple a Dirac field to the $U(1)$ potential, while this same
covariant derivative non-minimally couples the 3-form field to the charged
fermion. A number of properties are discussed in 5D; in particular, the
appearance of a topological fermionic current. A 4-dimensional reduced version
of the model is investigated and, { \bf in addition to the $U(1)$ electric- and
magnetic-sort of fields,} there emerges an extra set of electric- and
magnetic-like fields which contribute a negative pressure and may be identified
as a possible fraction of dark energy. The role of the topological fermionic
current is also contemplated upon dimensional reduction from 5D to 4D. Other
issues we present in 4 space-time dimensions are the emergence {\bf of a
pseudo-scalar massive particle,} an extra massive neutral gauge boson,{\bf
which we interpret as a kind of paraphoton}, and the calculation of spin- and
velocity-dependent interparticle potentials associated to the exchange of the
intermediate bosonic fields of the model.
