  Low-temperature ($T$) thermodynamic properties in magnetic fields ($B$) of
the quasi-Kagome antiferromagnet CePdAl ($T_{\rm N}\sim$ 2.7 K) were studied by
means of magnetization and specific-heat $C(T,B)$ measurements. The unusual
magnetic phase diagram, including three thermodynamic phases I-III, and
crossover anomalies, has been obtained. In low-field phase I, the existence of
the partial Kondo screening state on the one-third Ce sites is supported from
the thermodynamic point of view: (i) an appearance of the paramagnetic moment
with one-third of the full moment around 3 T, and (ii) an occurrence of the
entropy release $\sim$0.3$R$ln2 around the observed crossover. On the other
hand, a strong enhancement of $C/T$ is found around the point, where $T_{\rm
N}(B)$ meets the boundary of phase III, indicating the possible presence of a
tri-critical point. Furthermore, it is suggested that the three metamagnetic
transitions at $B_{{\rm m}i}$ ($i=$1,2,3) come from successive increments of
the Ising-type magnetic moment along the $c$-axis. In high-field state above 20
T, the behavior of $f$ electron can be rather described by the
crystal-electric-field model.
