In this article, an immiscible two-phase flow in two dimensional ordinary and modified T-junction microchannels is numerically studied. To this approach, the Lattice Boltzmann method with Pseudo-Potential model is used. The accuracy of the present model is examined by the Laplace test, drop contact angle, and drop formation in an ordinary T-junction microchannel. The comparison shows that the present results have good agreement with previous numerical and experimental data. The effects of various parameters including Capillary number, flow rate ratio, width ratio, and drop contact angle on the width of the drop and on the distance between drops for ordinary and modified T-junction microchannels are investigated in details. The results reveal that by simple modifications to the ordinary T-junction, smaller drops and lower distances between them are generated in the comparison of ordinary T-junction geometry under the same conditions. On the other hand, this study demonstrates that the multiphase flows in micro-devices are very sensitive to even small changes in the channel geometry. It also indicates that lattice Boltzmann method with Pseudo-Potential model is an effective numerical technique to simulate the generation of drops in microchannels.