The plasma produced by frequency mixing of an ultrafast pulsed laser and its second-harmonic field in air is a promising, table-top source of terahertz radiation. To maximize the generation efficiency of such a source, multi-parameter optimization is essential. A parametric study involving various external controls is presented here. Starting from the optimization of phase and polarization of the second-harmonic field, the effect of laser intensity on the terahertz flux is reported. Moreover, the effect of external focusing conditions, such as focal length of the lens and effect of laser beam aperture, is explored in detail. Contrary to the previous reports, we find that with the increase of laser intensity, terahertz (THz) flux increases with more conversion efficiency; this is attributed to the multiple ionization of the air, leading to stacked release of contributory electrons. Exploration of beam convergence reveals that relatively weaker focusing leads to increased terahertz production compared to sharp focusing conditions. Moreover, temporal characterization of the emitted terahertz pulse conducted using electro-optic sampling provides pulse duration of 368 fs with corresponding frequency spectra up to 3.6 THz. The maximum electric field of the terahertz pulse is estimated to be 1.12 MV cm−1 in our experimental conditions. Results of 2D particle-in-cell simulations are also presented with the objective of validating the role of transient photocurrent mechanism in THz generation from two-color laser-induced gas plasma. We believe the broadband, bright THz source presented here will be useful in the imaging of bigger samples as well as nonlinear spectroscopy.