This paper presents a scheme of THz generation by nonlinear photomixing of two cosh-Gaussian lasers pulses having different frequencies (ω1, ω2) and wave numbers $(\vec k_1, \vec k_2 )$ and same electrical field amplitude in a corrugated plasma embedded with transverse static magnetic field. Cosh-Gaussian laser pulses have steep gradient in intensity profile along with wider cross-section, which exerts a stronger nonlinear ponderomotive force at ω1 − ω2 and $\vec k_1 - \vec k_2 $ on plasma electrons imparting a nonlinear oscillatory velocity to plasma electrons. Oscillatory plasma electrons couple with the density ripple n′ = nα0eiαx to produce a nonlinear current, which is responsible for resonant THz radiation at frequency $\sim\left( {{\rm \omega} _{\rm c}^2 + {\rm \omega} _{\rm p}^2} \right)^{1/2} $. The amplitude, efficiency and beam quality of THz radiation can be optimized by choosing proper corrugation factor (α of the plasma), applied magnetic field (ωc), decentered parameter (b), and beam width parameter a0 of cosh-Gaussian lasers. An efficiency of $\sim\!10^{ - 2} - 10^{ - 1} $ is achieved for laser electric field E = 3.2 × 109 V/cm.