  Superconductivity and magnetism are competing effects that can coexist in
certain regimes. Their co-existence leads to unexpected new behaviors that
include the onset of exotic electron pair mechanisms and topological phases. In
this work, we study the properties of a Josephson junction between two
spin-split superconductors. The spin-splitting in the superconductors can arise
from either the coupling to a ferromagnetic material or an external magnetic
field. The properties of the junction are dominated by the Andreev bound states
that are also split. One of these states can cross the superconductor's Fermi
level, leading to a ground state transition characterized by a suppressed
supercurrent. We interpret the supercurrent blockade as coming from a dominance
of p-wave pairing close to the junction, where electrons at both sides of the
junction pair. To support this interpretation, we analyze the different pairing
channels and show that p-wave pairing is favored in the case where the
magnetization of the two superconductors is parallel and suppressed in the
anti-parallel case. We also analyze the noise spectrum that shows signatures of
the ground state transition in the form of an elevated zero-frequency noise.
