  We reveal that in a magnetically polarized medium, a specific commensurate
triplet pair density wave (TPDW) superconducting (SC) state, the staggered
d-wave $\Pi$-triplet state, may coexist with homogeneous triplet SC states and
even dominate eliminating them under generic conditions. When only this TPDW SC
state is present, we have the remarkable phenomenon of gapless
superconductivity. This may explain part of the difficulties in the realization
of the engineered localized Majorana fermion modes for topological quantum
computation. We point out qualitative characteristics of the tunneling density
of states, specific heat and charge susceptibility that identify the accessible
triplet SC regimes in a spinless medium.
