  A planar Maxwell-Chern-Simons-Proca model endowed with a Lorentz-violating
background is taken as framework to investigate the electron-electron
interaction. The Dirac sector is introduced exhibiting a Yukawa and a minimal
coupling with the scalar and the gauge fields, respectively. The the
electron-electron interaction is then exactly evaluated as the Fourier
transform of the Moller scattering amplitude (carried out in the
non-relativistic limit) for the case of a purely time-like background. The
interaction potential exhibits a totally screened behavior far from the origin
as consequence of massive character of the physical mediators. The total
interaction (scalar plus gauge potential) can always be attractive, revealing
that this model may lead to the formation of electron-electron bound states.
