Decompositions of matrices into potent and square-zero matrices

In order to find a suitable expression of an arbitrary square matrix over finite commutative ring, we prove that every such is always representable as sum potent and nilpotent at most two when the Jacobson radical ring has zero-square. This somewhat extends results ours in Linear Multilinear Algebra (2022) established for matrices considered on fields. Our main theorem also improves recent due Abyzov et al. Mat. Zametki (2017), Šter Appl. (2018) Shitov Indag. Math. (2019).