  We discuss the $U(1)$ gauged version of the 3+1 dimensional Faddeev-Skyrme
model supplemented by the Maxwell term. We show that there exist axially
symmetric static solutions coupled to the non-integer toroidal flux of magnetic
field, which revert to the usual Hopfions ${\cal A}_{m,n}$ of lower degrees
$Q=mn$ in the limit of the gauge coupling constant vanishing. The masses of the
static gauged Hopfions are found to be less than the corresponding masses of
the usual ungauged solitons ${\cal A}_{1,1}$ and ${\cal A}_{2,1}$ respectively,
they become lighter as gauge coupling increases. The dependence of the
solutions on the gauge coupling is investigated. We find that in the strong
coupling regime the gauged Hopfion carries two magnetic fluxes, which are
quantized in units of $2\pi$, carrying $n$ and $m$ quanta respectively. The
first flux encircles the position curve and the second one is directed along
the symmetry axis. Effective quantization of the field in the gauge sector may
allow us to reconsider the usual arguments concerning the lower topological
bound in the Faddeev-Skyrme-Maxwell model.
