  Synthesis of new materials that can host magnetic skyrmions and their
thorough experimental and theoretical characterization are essential for future
technological applications. The $\beta$-Mn-type compound FePtMo$_3$N is one
such novel material that belongs to the chiral space group $P4_132$, where the
antisymmetric Dzyaloshinkii-Moriya interaction is allowed due to the absence of
inversion symmetry. We report the results of small-angle neutron scattering
(SANS) measurements of FePtMo$_3$N and demonstrate that its magnetic ground
state is a long-period spin helix with a Curie temperature of 222~K. The
magnetic field-induced redistribution of the SANS intensity showed that the
helical structure transforms to a lattice of skyrmions at $\sim$13~mT at
temperatures just below $T_{\text C}$. Our key observation is that the skyrmion
state in FePtMo$_3$N is robust against field cooling down to the lowest
temperatures. Moreover, once the metastable state is prepared by field cooling,
the skyrmion lattice exists even in zero field. Furthermore, we show that the
skyrmion size in FePtMo$_3$N exhibits high sensitivity to the sample
temperature and can be continuously tuned between 120 and 210~nm. This offers
new prospects in the control of topological properties of chiral magnets.
