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In polar magnets, such as GaV$_4$S$_8$, GaV$_4$Se$_8$ and VOSe$_2$O$_5$, modulated magnetic phases namely the cycloidal and the N\'eel-type skyrmion lattice states were identified over extended temperature ranges, even down to zero Kelvin. Our combined small-angle neutron scattering and magnetization study shows the robustness of the N\'eel-type magnetic modulations also against magnetic fields up to 2 T in the polar GaMo$_4$S$_8$. In addition to the large upper critical field, enhanced spin-orbit coupling produces a variety of modulated phases with sub-10 nm periodicity and a peculiar distribution of the magnetic modulation vectors. Thus, our work demonstrates that non-centrosymmetric magnets with $4d$ and $5d$ electron systems are ideal candidates to host highly compressed magnetic spirals and skyrmions.