  We theoretically study the spectral properties of a one dimensional
semiconductor-superconductor-ferromagnetic insulator (SE-SU-FMI) hybrid
nanostructure, motivated by recents experiments where such devices have been
fabricated using epitaxial growing techniques. We model the hybrid structure as
a one-dimensional single-channel semiconductor nanowire under the simultaneous
effect of two proximity-induced interactions: superconducting pairing and a
(spatially inhomogeneous) Zeeman exchange field. The coexistence of these
competing interactions generates a rich quantum phase diagram and a complex
subgap Andreev bound state (ABS) spectrum. By exploiting the symmetries of the
problem, we classify the solutions of the Bogoliubov-de Gennes equations into
even and odd ABS with respect to the spatial inversion symmetry $x\to -x$. We
find the ABS spectrum of the device as a function of the different parameters
of the model: the length $L$ of the coexisting SU-FMI region, the induced
Zeeman exchange field $h_0$, and the induced superconducting coherence length
$\xi$. In particular we analyze the evolution of the subgap spectrum as a
function of the length $L$. Interestingly, we have found that depending on the
ratio $h_0/\Delta$, the emerging ABS can eventually cross below the Fermi
energy at certain critical values $L_c$, and induce spin-and fermion
parity-changing quantum phase transitions. We argue that this type of device
constitute a promising highly-tunable platform to engineer subgap ABS.
