We present a further development of methods for analytical calculations of Green's functions of lattice fermions based on recurrence relations. Applying it to tight-binding systems and topological superconductors in different dimensions we obtain a number of new results. In particular we derive an explicit expression for arbitrary Green's function of an open Kitaev chain and discover non-local fermionic corner states in a 2D p-wave superconductor. PACS numbers: 73.20.-r, 71.15.-m, 71.20.-b, 02.10.Yn arXiv:1706.06463v1 [cond-mat.mes-hall]