In this work, we introduce a novel version of Padovan and Perrin numbers which we refer to as non-Newtonian Padovan and non-Newtonian Perrin numbers. Furthermore, we examine about a number of their properties. Additionally, we provide a variety of identities and formulas involving these new kinds, including the Binet-like formulas, the generating functions, the partial sum formulas, and the binomial sum formulas.