In this paper, we have studied the electrokinetics and mixing driven by an imposed pressure gradient and electric field in a charged modulated microchannel. By performing detailed numerical simulations based on the coupled Poisson, Nernst–Planck, and incompressible Navier–Stokes equations, we discussed electrokinetic transport and other hydrodynamic effects under the application of combined pressure and dc electric fields for different values of electric double layer thickness and channel patch potential. A numerical method based on the pressure correction iterative algorithm is adopted to compute the flow field and mole fraction of the ions. Since electroosmotic flow depends on the magnitude and sign of wall potential, a vortex can be generated through adjusting the patch potential. The dependence of the vortical flow on imposed pressure gradient is investigated. Formation of vortex in electroosmotic flow has importance in producing solute dispersion. The circulation of vortex grows with the rise of patch potential, whereas the pressure-assisted electroosmotic flow produces a reduction in vortex size. However, the flow rate is substantially increased in pressure-assisted electroosmotic flow. Flow reversal and suppression of fluid transport is possible through an adverse pressure gradient. The ion distribution and electric field above the potential patch are distorted by the imposed pressure gradient. At higher values of the pressure gradient, the combined pressure electroosmotic-driven flow resembles the fully developed Poiseuille flow. Current density is found to increase with the rise of imposed pressure gradient.