  In this work, we study a $U(1) \times U(1) ^{\prime}-$ model that results
from a dimensional reduction of the N=1-D=4 supersymmetric version of the
Cremer-Scherk-Kalb-Ramond model with non-minimal coupling to matter. Field
truncations are not carried out, two Abelian symmetries coexist and three
vector fields are present; two of them are gauge bosons. Then, by considering
the full $N=2-D=3$ supersymmetric model, we study the mechanism for magnetic
vortex formation by means of the Bogomol'nyi relations, the magnetic flux and
the topological charge in the presence of the two gauge potentials. A short
discussion on the relation between our $N=2-D=3$ supersymmetric model and
vortices in superfluid films is also presented.
