  The non-trivial magnetic texture in real space gives rise to the intriguing
phenomenon of topological Hall effect (THE), which is relatively less explored
in topological semimetals. Here, we report large THE in the antiferromagnetic
(AFM) state in single crystals of EuAgAs, an AFM Dirac semimetal. EuAgAs hosts
AFM ground state below $T_N$ = 12 K with a weak ferromagnetic component. The
in-plane isothermal magnetization below $T_N$ exhibits a weak metamagnetic
transition. We also observe chiral anomaly induced positive longitudinal
magnetoconductivity which indicates a Weyl fermion state under applied magnetic
field. The first-principles calculations reveal that EuAgAs is an AFM Dirac
semimetal with a pair of Dirac cones, and therefore, a Weyl semimetailic state
can be realized under time-reversal symmetry breaking via an applied magnetic
field. Our study establishes that EuAgAs is a novel system for exploiting the
interplay of band topology and the topology of the magnetic texture.
