  In this paper, we consider a massive charged fermionic quantum field and
investigate the current densities induced by a magnetic flux running along the
core of an idealized cosmic string in the background geometry of a
5-dimensional anti-de Sitter spacetime, assuming that an extra dimension is
compactified. Along the compact dimension quasi-periodicity condition is
imposed on the field with a general phase. Moreover, we admit the presence of a
magnetic flux enclosed by the compactified axis. The latter gives rise to
Ahanorov-Bohm-like effect on the vacuum expectation value of the currents. In
this setup, only azimuthal and axial current densities take place. The former
presents two contributions, with the first one due to the cosmic string in a
5-dimensional AdS spacetime without compact dimension, and the second one being
induced by the compactification itself. The latter is an odd function of the
magnetic flux along the cosmic string and an even function of the magnetic flux
enclosed by the compactified axis with period equal to the quantum flux. As to
the induced axial current, it is an even function of the magnetic flux along
the string's core and an odd function of the magnetic flux enclosed by the
compactification perimeter. For untwisted and twisted field along compact
dimension, the axial current vanishes. The massless field case is presented as
well as some asymptotic limits for the parameters of the model.
