  The quest of exo-Earths has become a prominent field. In this work, we study
the stability of non-coplanar planetary configurations consisting of an
inclined inner terrestrial planet in mean-motion resonance with an outer giant
planet. We examine the families of circular and elliptic symmetric periodic
orbits with respect to the vertical stability, and identify the vertical
critical orbits from which the spatial families emanate. We showcase that
stable spatial periodic orbits can exist for both prograde and retrograde
motion in 3/2, 2/1, 5/2, 3/1, 4/1 and 5/1 resonances for broad ranges of
inclinations, when the giant evolves on a circular orbit. When the orbit of the
giant is elliptic, only the 2/1 resonance has stable periodic orbits up to high
inclinations, while the 3/1, 4/1 and 5/1 resonances possess segments of
stability for low inclinations. Furthermore, we show that regular motion can
also take place in the vicinity of both horizontally and vertically stable
planar periodic orbits, even for very high inclinations. Finally, the results
are discussed in the context of asteroid dynamics.
