Non-standard interactions (NSI) of the neutrino sector is studied in the framework of coherent elastic neutrino-nucleus scattering (CE nu NS). Differential and total cross sections of the CE nu NS process for several nuclei are presented for different scale of incoming neutrino energy. Behavior of form factor in accordance with the criteria of coherency process is also shown as a function of momentum transfer. Several benchmarks were implemented according to the proposed advancement of CE nu NS experiments. Using recently analyzed bound, we forecast that the NSI cross section spectrum is larger than the standard model (SM) ones and increased for heavier nuclei. Prediction of the NSI bounds is also given in the parameter space of the new interaction strengths by utilizing the deviation of NSI and SM spectrum ratio. All possibilities of non-universal flavor conserving (FC) and flavor violating (FV) process are considered as neutrino interact with the quark constituent of nucleus.