  We investigate the effects of a brane and magnetic-flux-carrying cosmic
string on the vacuum expectation value (VEV) of the current density for a
charged fermionic field in the background geometry of 4+1 dimensional anti-de
Sitter (AdS) spacetime. The brane is parallel to the AdS boundary and the
cosmic string is orthogonal to the brane. Two types of boundary conditions are
considered on the brane that include the MIT bag boundary condition and the
boundary conditions in Z2-symmetric braneworld models. The brane divides the
space into two regions with different properties of the vacuum state. The only
nonzero component of the current density is along the azimuthal direction and
in both the regions the corresponding VEV is decomposed into the brane-free and
brane-induced contributions. The latter vanishes on the string and near the
string the total current is dominated by the brane-free part. At large
distances from the string and in the region between the brane and AdS horizon
the decay of the brane-induced current density, as a function of the proper
distance, is power-law for both massless and massive fields. For a massive
field this behavior is essentially different from that in the Minkowski bulk.
In the region between the brane and AdS boundary the large-distance decay of
the current density is exponential. Depending on the boundary condition on the
brane, the brane-induced contribution is dominant or subdominant in the total
current density at large distances from the string. By using the results for
fields realizing two inequivalent irreducible representations of the Clifford
algebra, the vacuum current density is investigated in C- and P-symmetric
fermionic models. Applications are given for a cosmic string in the
Randall-Sundrum-type braneworld model with a single brane.
