  We present a theoretical study of the interplay between topological p-wave
superconductivity, orbital magnetic fields and quantum Hall phases in coupled
wire systems. First, we calculate the phase diagram and physical observables of
a fermionic ladder made of two coupled Kitaev chains, and discuss the presence
of two and four Majorana zero modes. Second, we analyze hybrid systems
consisting of a Kitaev chain coupled to a Luttinger liquid. By tuning the
magnetic field and the carrier density, we identify quantum Hall and charge
density wave phases, as well as regimes in which superconductivity is induced
in the second chain by proximity effect. Finally, we consider two-dimensional
systems made of weakly coupled ladders. There, we engineer a $p+ip$
superconductor and describe a generalization of the $\nu=1/2$ fractional
quantum Hall phase. These phases might be realized in solid-state or cold-atom
nanowires.
