  In this paper, we analyse the bosonic current densities induced by a magnetic
flux running along an idealized cosmic string in a high-dimensional spacetime,
admitting that the coordinate along the string's axis is compactified.
Additionally we admit the presence of an magnetic flux enclosed by the
compactification axis. In order to develop this analysis we calculate the
complete set of normalized bosonic wave-functions obeying a quasiperiodicity
condition, with arbitrary phase $\beta$, along the compactified dimension. In
this context, only azimuthal and axial currents densities take place. As to the
azimuthal current, two contributions appear. The first contribution corresponds
to the standard azimuthal current in a cosmic string spacetime without
compactification, while the second contribution is a new one, induced by the
compactification itself. The latter is an even function of the magnetic flux
enclosed by the string axis and is an odd function of the magnetic flux along
its core with period equal to quantum flux, $\Phi_0=2\pi/e$. On the other hand,
the nonzero axial current density is an even function of the magnetic flux
along the core of the string and an odd function of the magnetic flux enclosed
by it. We also find that the axial current density vanishes for untwisted and
twisted bosonic fields in the absence of the magnetic flux enclosed by the
string axis. Some asymptotic expressions for the current density are provided
for specific limiting cases of the physical parameter of the model.
