  We consider a Josephson junction consisting of superconductor/ferromagnetic
insulator (S/FI) bilayers as electrodes which proximizes a nearby 2D electron
gas. By starting from a generic Josephson hybrid planar setup we present an
exhaustive analysis of the the interplay between the superconducting and
magnetic proximity effects and the conditions under which the structure
undergoes transitions to a non-trivial topological phase. We address the 2D
bound state problem using a general transfer matrix approach that reduces the
problem to an effective 1D Hamiltonian. This allows for straightforward study
of topological properties in different symmetry classes. As an example we
consider a narrow channel coupled with multiple ferromagnetic superconducting
fingers, and discuss how the Majorana bound states can be spatially controlled
by tuning the superconducting phases. Following our approach we also show the
energy spectrum, the free energy and finally the multiterminal Josephson
current of the setup.
