  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 proximitized superconducting (S) and
ferromagnetic (F) surfaces. This consists of the derivation of the Green's
functions for each region by the asymptotic solutions method, and their
coupling by a tight-binding Hamiltonian with the Dyson equation to obtain the
full Green's functions of the system. These functions allow the direct
calculation of the momentum-resolved spectral density of states, the
identification of subgap interface states, and the derivation of the
differential conductance for a wide variety of configurations of the junctions.
We illustrate the application of this method for some simple systems with two
and three regions, finding the characteristic chiral state of the Quantum
Anomalous Hall Effect (QAHE) at the NF interfaces, and chiral Majorana modes at
the NS interfaces. Finally, we discuss some geometrical effects present in
three-region junctions such as weak Fabry-P\'erot resonances and Andreev bound
states.
