  Two-dimensional moir\'e materials provide a highly tunable platform to
investigate strongly correlated electronic states. Such emergent many-body
phenomena can be optically probed in moir\'e systems created by stacking two
layers of transition metal dichalcogenide semiconductors: optically injected
excitons can interact with itinerant carriers occupying narrow moir\'e bands to
form exciton-polarons sensitive to strong correlations. Here, we investigate
the behaviour of excitons dressed by a Fermi sea localised by the moir\'e
superlattice of a molybdenum diselenide (MoSe$_2$) / tungsten diselenide
(WSe$_2$) twisted hetero-bilayer. At a multitude of fractional fillings of the
moir\'e lattice, we observe ordering of both electrons and holes into stable
correlated electronic states. Magneto-optical measurements reveal extraordinary
Zeeman splittings of the exciton-polarons due to exchange interactions in the
correlated hole phases, with a maximum close to the correlated state at one
hole per site. The temperature dependence of the Zeeman splitting reveals
antiferromagnetic ordering of the correlated holes across a wide range of
fractional fillings. Our results illustrate the nature of exciton-polarons in
the presence of strongly correlated electronic states and reveal the rich
potential of the MoSe$_2$/WSe$_2$ platform for investigations of Fermi-Hubbard
and Bose-Hubbard physics.
