This work presents a Green’s function approach, originally implemented in graphene with well-defined edges, to the surface of a strong 3D Topological Insulator (TI) with a sequence of proximitizedsuperconducting (S) and ferromagnetic (F) surfaces. This consists of the derivation of the Green’sfunctions for each region by the asymptotic solutions method, and their coupling by a tight-bindingHamiltonian with the Dyson equation to obtain the full Green’s functions of the system. Thesefunctions allow the direct calculation of the momentum-resolved spectral density of states, the iden-tification of subgap interface states, and the derivation of the differential conductance for a widevariety of configurations of the junctions. We illustrate the application of this method for somesimple systems with two and three regions, finding the characteristic chiral state of the QuantumAnomalous Hall Effect (QAHE) at the NF interfaces, and chiral Majorana modes at the NS inter-faces. Finally, we discuss some geometrical effects present in three-region junctions such as weakFabry-P ́erot resonances and Andreev bound states.