Two-color strong-field photoionization of two diatomic molecules (N$_2$, CO) is studied using a Velocity Map Imaging (VMI) spectrometer. The fundamental frequency, along with the second harmonic (800 + 400 nm) at different phases, with the two different polarization schemes viz, orthogonal and parallel, is employed for measuring the ion yields and photoelectron momentum distributions. The yield of the parent ion and its charged fragments as a function of the phase difference between the two-color field has been studied thoroughly, and the results are presented here. The correlation trends of the parent ion with their fragments as a function of the relative phase are discussed. It is observed that the ionized CO and its fragments have different correlation trends at different polarization schemes. Additionally, the photoelectron momentum distribution of N$_2$ and CO due to orthogonal two-color (OTC) and parallel two-color (PTC) is performed in order to understand the modulation of electron dynamics as a function of phase between 800 nm and 400nm. Further, the asymmetry parameter as a function of electron momenta due to the two-color fields has been estimated and discussed.