We study magnetized accretion shock flows using the relativistic equation of state having variable adiabatic index (Γ). We include bremsstrahlung and cyclotron cooling for the neutron star which has very strong dipole-like magnetic field and is aligned with the rotation axis of the star. We find all possible accretion solutions. All accretion solutions terminate with a shock very near to the star surface and the height of this primary shock does not vary considerably either with the spin period or the Bernoulli parameter of the flow, although the strength of the shock may vary with the period. For moderately rotating central star there is a possible formation of multiple sonic points in the flow and there a second shock far away from the surface of the star. We find that if the rotation period is less than a certain value, then multiple critical points or internal shocks are not possible, but this value depends upon the composition of the flow. We also find that cooling effect dominates after the shock and for consistent accretion solutions cyclotron cooling should be present along with the bremsstrahlung cooling.