  In this paper we analyse the vacuum fluctuations of quantum fermionic current
densities, $<j^A(x)>$, induced by a magnetic flux running along the core of the
conical space produced by the presence of cosmic string, in a
$(1+d)-$dimensional bulk, for $2\leq d\leq 5$. In order to develop this
investigation we construct an expression for the fermionic propagator, which
can be applied for those different dimensions of the spacetime. Two specific
analysis for the induced current densities are presented: $(i)$ for massless
fields in three and four dimensions, and $(ii)$ for massive fields in all
dimensions considered. In the latter specific values for the parameters which
codify the presence of the cosmic string and the fractional part of the ratio
of the magnetic flux by the quantum one are considered. Although being a very
special situation and somewhat unnatural, the corresponding analysis of induced
fermionic current densities under this circumstance may shed light on the
qualitative behavior of these quantities in a more general situation.
