  In this paper, we consider a charged massive fermionic quantum field in the
idealized cosmic string spacetime and in the presence of a magnetic field
confined in a cylindrical tube of finite radius. Three distinct configurations
for the magnetic fields are taken into account: (i) a cylindrical shell of
radius $a$, (ii) a magnetic field proportional to $1/r$ and (iii) a constant
magnetic field. In these three cases, the axis of the infinitely long tube of
radius $a$ coincides with the cosmic string. Our main objectives in this paper
are to analyze the fermionic condensat (FC) e and the vacuum expectation value
(VEV) of the fermionic energy-momentum tensor. In order to do that, we
explicitly construct the complete set of normalized wave-functions for each
configuration of magnetic field. We show that in the region outside the tube,
the FC and the VEV of the energy-momentum tensor are decomposed into two parts:
the first ones correspond to the zero-thickness magnetic flux contributions,
and the seconds are induced by the non-trivial structure of the magnetic field,
named core-induced contributions. The latter present specific forms depending
on the magnetic field configuration considered. We also show that the VEV of
the energy-momentum tensor is diagonal, obeys the conservation condition and
its trace is expressed in terms of the fermionic condensate. The zero-thickness
contributions to the FC and VEV of the energy-momentum tensor, depend only on
the fractional part of the ration of the magnetic flux inside the tube by the
quantum one. As to the core-induced contributions they depend on the total
magnetic flux inside the tube, and consequently, in general, are not a periodic
function of the magnetic flux.
