  The Weyl semimetal CeAlGe is a promising material to study nontrivial
topologies in real and momentum space due to the presence of a topological
magnetic phase. Our results at ambient pressure show that the electronic
properties of CeAlGe are extremely sensitive to small stoichiometric
variations. In particular, the topological Hall effect (THE) present in CeAlGe
is absent in some samples of almost identical chemical composition. The
application of external pressure favors the antiferromagnetic ground state. It
also induces a THE where it was not visible at ambient pressure. Furthermore, a
small pressure is sufficient to drive the single region of the THE in magnetic
fields into two different ones. Our results reveal an extreme sensitivity of
the electronic properties of CeAlGe to tiny changes in its chemical
composition, leading to a high tunability by external stimuli. We can relate
this sensitivity to a shift in the Fermi level and to domain walls.
