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A<sc>bstract</sc> We report multi-differential measurements of strange hadron production ranging from mid- to target-rapidity in Au+Au collisions at a center-of-momentum energy per nucleon pair of$$ \sqrt{s_{\textrm{NN}}} $$ $\sqrt{s_{\mathrm{NN}}}$= 3 GeV with the STAR experiment at RHIC.$$ {K}_S^0 $$ $K_S^0$meson and Λ hyperon yields are measured via their weak decay channels. Collision centrality and rapidity dependences of the transverse momentum spectra and particle ratios are presented. Particle mass and centrality dependence of the average transverse momenta of Λ and$$ {K}_S^0 $$ $K_S^0$are compared with other strange particles, providing evidence of the development of hadronic rescattering in such collisions. The 4πyields of each of these strange hadrons show a consistent centrality dependence. Discussions on radial flow, the strange hadron production mechanism, and properties of the medium created in such collisions are presented together with results from hadronic transport and thermal model calculations.