  For a $(3+1)$-dimensional generalization of the Schwinger model, we compute
the interaction energy between two test charges. The result shows that the
static potential profile contains a linear term leading to the confinement of
probe charges, exactly as in the original model in two dimensions. We further
show that the same 4-dimensional model also appears as one version of the $ B
\wedge F$ models in $(3+1)$ dimensions under dualization of Stueckelberg-like
massive gauge theories. Interestingly, this particular model is characterized
by the mixing between a $U(1)$ potential and an Abelian $3$-form field of the
type that appears in the topological sector of QCD.
