Using electromagnetic treatment, an expression of effective nonlinear optical susceptibility χ_e =χ_e⁽²⁾+χ_e⁽³⁾E is obtained for III-V semiconducting crystals in an applied transverse dc magnetic field under off-resonant transition regime. The origin of nonlinear interaction lies in nonlinear polarization arising from the crystal properties such as piezoelectricity and electrostriction. Numerical estimates have been made by a representative n-InSb crystal at 77K duly irradiated by a pulsed 10.6-μm CO₂ laser under off-resonant transition regime. Efforts are dedicated to optimizing doping level and externally applied dc magnetic field to achieve maximum χ_e⁽²⁾ and χ_e⁽³⁾. The results are found to be in good agreement with the available literature. The analysis shows that χ_e⁽²⁾ and χ_e⁽³⁾ can be significantly enhanced in doped III--V semiconductors by the proper selection of doping concentration and dc magnetic field, which confirms its potential as a candidate material for the fabrication of nonlinear optical devices.