The recent realization of superconducting proximity effects in chiral antiferromagnets (cAFMs) opens a new route to nonreciprocal superconducting transport of fundamental interest and practical importance. Using microscopic modeling and symmetry analysis, we show that Josephson junctions formed by conventional s-wave superconductors (SCs) and cAFMs on the kagome lattice exhibit both Josephson diode effects and anomalous Josephson effects (a ϕ0-junction state with a finite supercurrent at zero phase bias) when spacial inversion \({\mathcal{I}}\), time-reversal \({\mathcal{T}}\), and the combined mirror-time-reversal \({{\mathcal{TM}}}_{z}\) symmetries are simultaneously broken. We propose two setups to realize these phenomena and achieve high diode efficiency. (i) An SC/cAFM/SC junction with spin-orbit coupling, which enables a field-free diode effect together with a tunable anomalous Josephson supercurrent. (ii) An SC/cAFM/\({{\rm{cAFM}}}^{{\prime} }\)/SC junction, where two cAFM layers with different in-plane order orientations, under an out-of-plane Zeeman field, produce a pronounced diode effect and anomalous Josephson response. These results establish a direct link between \({{\mathcal{TM}}}_{z}\) symmetry breaking and nonreciprocal superconductivity, suggesting cAFMs as versatile platforms for symmetry-engineered Josephson diodes and tunable ϕ0-junctions.
