  We study the ground-state phase diagram of two-component fermions loaded in a
ladder-like lattice at half filling in the presence of spin-orbit coupling. For
repulsive fermions with unidirectional spin-orbit coupling along the legs we
identify a N\'{e}el state which is separated from rung-singlet and
ferromagnetic states by Ising phase transition lines. These lines cross for
maximal spin-orbit coupling and a direct Gaussian phase transition between
rung-singlet and ferro phases is realized. For the case of Rashba-like
spin-orbit coupling, besides the rung singlet phases two distinct striped
ferromagnetic phases are formed. In case of attractive fermions with spin-orbit
coupling at half-filling for decoupled chains we identify a dimerized state
that separates a singlet superconductor and a ferromagnetic states.
