  We apply an inverse Compton $e^\pm$ pair cascade model for $\gamma$-ray
production in massive binary system LSI +61$^{\rm o}$ 303 assuming that
electrons are accelerated already inside the inner part of the jet launched by
the compact object. $\gamma$-ray spectra, affected by the cascade process, and
lower energy spectra, from the synchrotron cooling of the highest energy
electrons in the jet, are calculated as a function of the phase of this binary
system. $\gamma$-ray spectra expected in such model have different shape than
that ones produced by electrons in the jet directly to observer. Moreover, the
model predicts clear anti-correlation between $\gamma$-ray fluxes in the GeV
(1-10 GeV) and TeV ($>200$ GeV) energy ranges with the peak of the TeV emission
at the phase $\sim$0.5 (the peak half width ranges between the phases
$\sim$0.4-0.9 for the inclination of the binary system equal to $60^{\rm o}$,
and $\sim$0.4-0.1 for $30^{\rm o}$). The fine features of TeV $\gamma$-ray
emission (fluxes and spectral shapes) as a function of the phase of the binary
system are consistent with recent observations reported by the MAGIC
collaboration. Future simultaneous observations in the GeV energies (by the
GLAST and AGILE telescopes) and in the TeV energies (by the MAGIC and VERITAS
telescopes) should test other predictions of the considered model supporting or
disproving the hypothersis of acceleration of electrons already in the inner
part of the microquasar jets.
