  As exemplified by the growing interest in the quantum anomalous Hall effect,
the research on topology as an organizing principle of quantum matter is
greatly enriched from the interplay with magnetism. In this vein, we present a
combined electrical and thermoelectrical transport study on the magnetic Weyl
semimetal EuCd$_2$As$_2$. Unconventional contribution to the anomalous Hall and
anomalous Nernst effects were observed both above and below the magnetic
transition temperature of EuCd$_2$As$_2$, indicating the existence of
significant Berry curvature. EuCd$_2$As$_2$ represents a rare case in which
this unconventional transverse transport emerges both above and below the
magnetic transition temperature in the same material. The transport properties
evolve with temperature and field in the antiferromagnetic phase in a different
manner than in the paramagnetic phase, suggesting different mechanisms to their
origin. Our results indicate EuCd$_2$As$_2$ is a fertile playground for
investigating the interplay between magnetism and topology, and potentially a
plethora of topologically nontrivial phases rooted in this interplay.
