  The Casimir force between two short-range charge sources, embedded in a
background of one dimensional massive Dirac fermions, is explored by means of
the original $\ln\text{[Wronskian]}$ contour integration techniques. For
identical sources with the same (positive) charge, we find that in the
non-perturbative region the Casimir interaction between them can reach
sufficiently large negative values and simultaneously reveal the features of a
long-range force in spite of nonzero fermion mass, that could significantly
influence the properties of such quasi-one-dimensional QED systems. For large
distances $s$ between sources we recover that their mutual interaction is
governed first of all by the structure of the discrete spectrum of a single
source, in dependence on which it can be tuned to give an attractive, a
repulsive, or an (almost) compensated Casimir force with various rates of the
exponential fall-down, quite different from the standard $\exp (-2 m s)$ law.
By means of the same $\ln\text{[Wronskian]}$ techniques, the case of two
$\delta$-sources is also considered in a self-consistent manner with similar
results for the variability of the Casimir force. A quite different behavior of
the Casimir force is found for the antisymmetric source-anti-source system. In
particular, in this case, there is no possibility for a long-range interaction
between sources. The asymptotics of the Casimir force follows the standard
$\exp (-2 m s)$ law. Moreover, for small separations between sources, the
Casimir force for symmetric and antisymmetric cases turns out to be of opposite
sign.
