Notch signaling (NS) determines the fate of adjacent cells during metazoans development. This intercellular signaling mechanism regulates diverse development processes like cell differentiation, proliferation, survival and is considered responsible for maintaining cellular homeostasis. In this study, we elucidate the role of Notch heterogeneity (NH) in cell fate determination. We studied the role of NH at intercellular, intracellular and the coexistence of Notch variation simultaneously at the intracellular and intercellular level in direct cell-cell signaling on an irregular cell mosaic. In addition, the effect of intracellular Notch receptor diffusion on an irregular cell lattice is also taken into account during Delta-Notch lateral inhibition (LI) process. Through mathematical and computational models, we discovered that the classical checkerboard pattern formation can be reproduced with an accuracy of 70-81% by accounting for NH in a realistic epithelial layer of multicellular organisms.