  In this paper, we analyse the bosonic current densities induced by a magnetic
flux running along the core of an idealized cosmic string in a high-dimensional
AdS spacetime, admitting that an extra dimension coordinate is compactified.
Additionally we admit the presence of a magnetic flux enclosed by the
compactified 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 extra dimension. In this
context, only azimuthal and axial currents densities take place. As to the
azimuthal current, two contributions appear.
  The first one corresponds to the standard azimuthal current in
high-dimensional AdS spacetime with a cosmic string 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
compactified 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 the
compactified axis. 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 compactified axis. Some asymptotic expressions for the current
density are provided for specific limiting cases of the physical parameter of
the model.
