We present an original approach to realistic modeling of light focusing by microsphere systems to form the photonic jets for nano-patterning of the substrates with high refractive index. In simulations we analyze the photonic jets produced by a single sphere and close-packed array of microspheres on the photoresist layer and Si substrate. We show how the lithographic profiles can be controlled by varying the exposure dose and system geometry in wide ranges of photoresist layer thicknesses and microsphere sizes. The modeling covers the entire lithographic system and accounts for the interference of focused light transmitted through the microlenses and reflected from the Si substrate. We use our approach to optimize the size of the lithographic pattern and confirm the simulation results experimentally. The suggested set of methods is rather universal and may be applied to other microlens and resist materials to minimize lithography lateral resolution.