Using the classical hydrodynamic model of semiconductor plasmas, the parametric amplification and dispersion characteristics of optical phonon mode in a semiconductor magnetoplasma are investigated analytically. An expression for effective complex second-order optical susceptibility ($\chi^{(2)}_e=(\chi^{(2)}_e)_r+ \chi^{(2)}_e)_i)$ is obtained under off-resonant laser irradiation. The analysis deals with qualitative behaviour of threshold pump amplitude($\xi_{0,\rm{th}}$) for the onset of parametric excitation, anomalous parametric dispersion (via $(\xi^{(2)}_e)_r)$ and parametric gain coefficient ($g_{\rm{para}}$ via ($(\xi^{(2)}_e)_i)$ with respect to externally applied magnetostatic field ($B_0$) for different values of doping concentration ($n_0$). Numerical estimates are made for n-InSb–CO$_2$ laser system at 77 K. The analysis offers three achievable resonance conditions at which $\xi_{0,\rm{th}}$ reduces whereas $g_{\rm{para}}$ enhances by two orders of magnitude. The lowering in $\xi_{0,\rm{th}}$ and enhancement in $g_{\rm{para}}$, under proper selection of $B_0$ and $n_0$, confirms the chosen nonlinear medium as a potential candidate material for the fabrication of efficient optical parametric amplifiers. The negative and positive enhanced parametric dispersion may be of potential use in the study of squeezed state generation as well as in group velocity dispersion in semiconductor magnetoplasmas.