  The kurtosis and skewness of net baryon-number fluctuations are studied for
the magnetized phase diagram of three-flavor quark matter within the Polyakov
extended Nambu$-$Jona-Lasinio model. Two models with magnetic catalysis and
inverse magnetic catalysis are considered. Special attention is given to their
behavior in the neighborhood of the light and strange critical end points
(CEPs). Several isentropic trajectories that come close the CEPs are studied in
order to analyze possible signatures of a CEP in the presence of external
magnetic fields. The effect of the magnetic field on the velocity of sound,
$v_s^2$, when both the light and strange CEPs are approached from the crossover
region is also investigated by calculating their temperature and baryon
chemical potential dependencies at fixed distances from these CEPs. Regions
with large fluctuations but no CEP in nonmagnetized matter develop a CEP under
the action of a strong magnetic field. Besides, the Landau quantization of the
quark trajectories may result in the appearance of extra CEPs, in particular,
in the strange sector for strong magnetic fields, identifiable by the net
baryon-number fluctuations. Stiffer (smoother) fluctuations in the region of
the CEP are characteristic of models that do not predict (do predict) the
inverse magnetic catalysis at zero chemical potential. Particularly interesting
is the ratio $\chi^4_B/\chi^2_B$ that has a more pronounced peak structure,
indicating that it is eventually a more convenient probe for the search of a
CEP. The speed of sound shows a much richer structure in magnetized quark
matter and allows one to identify both chiral and deconfinement transitions.
