  We predict that spatially modulated Zeeman splitting resulting in the
formation of Zeeman lattice can be used for creation of localized
self-sustained excitations in spinor polariton condensates with dominant
repulsive interactions. In such lattices, the phenomenon of TE-TM splitting,
playing the role of effective spin-orbit interaction, leads to the emergence of
the stripe phase and formation of stable gap-stripe solitons with complex
intrinsic structure resulting from the presence of two characteristic spatial
scales, one of which is set by the period of Zeeman lattice, while other is set
by the momentum in the depth of the Brillouin zone, at which such solitons
bifurcate from the linear spectrum. Gap-stripe polariton solitons can be
excited by suitable resonant pump.
