  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 $\dot P =
5.3\times 10^{-10}$ 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.
