We report on the follow-up $XMM-Newton$ observation of the persistent X-ray pulsar CXOU J225355.1+624336, discovered with the CATS@BAR project on archival $Chandra$ data. The source was detected at $f_{rm X}$(0.5-10 keV) = 3.4$times 10^{-12}$ erg cm$^{-2}$ s$^{-1}$, a flux level which is fully consistent with the previous observations performed with $ROSAT$, $Swift$, and $Chandra$. The measured pulse period $P$ = 46.753(3) s, compared with the previous measurements, implies a constant spin down at an average rate $dot P = 5.3times 10^{-10}$ s s$^{-1}$. The pulse profile is energy dependent, showing three peaks at low energy and a less structured profile above about 3.5 keV. The pulsed fraction slightly increases with energy. We described the time-averaged EPIC spectrum with four different emission models: a partially covered power law, a cut-off power law, and a power law with an additional thermal component (either a black body or a collisionally ionized gas). In all cases we obtained equally good fits, so it was not possible to prefer or reject any emission model on the statistical basis. However, we disfavour the presence of the thermal components, since their modeled X-ray flux, resulting from a region larger than the neutron star surface, would largely dominate the X-ray emission from the pulsar. The phase-resolved spectral analysis showed that a simple flux variation cannot explain the source variability and proved that it is characterized by a spectral variability along the pulse phase. The results of the $XMM-Newton$ observation confirmed that CXOU J225355.1+624336 is a BeXB with a low-luminosity ($L_{rm X} sim 10^{34-35}$ erg s$^{-1}$), a limited variability, and a constant spin down. Therefore, they reinforce the source classification as a persistent BeXB.
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