  We report the first multi-differential measurements of strange hadrons of
$K^{-}$, $\phi$ and $\Xi^{-}$ yields as well as the ratios of $\phi/K^-$ and
$\phi/\Xi^-$ in Au+Au collisions at ${\sqrt{s_{\rm NN}} = \rm{3\,GeV}}$ with
the STAR experiment fixed target configuration at RHIC. The $\phi$ mesons and
$\Xi^{-}$ hyperons are measured through hadronic decay channels,
$\phi\rightarrow K^+K^-$ and $\Xi^-\rightarrow \Lambda\pi^-$. Collision
centrality and rapidity dependence of the transverse momentum spectra for these
strange hadrons are presented. The $4\pi$ yields and ratios are compared to
thermal model and hadronic transport model predictions. At this collision
energy, thermal model with grand canonical ensemble (GCE) under-predicts the
$\phi/K^-$ and $\phi/\Xi^-$ ratios while the result of canonical ensemble (CE)
calculations reproduce $\phi/K^-$, with the correlation length $r_c \sim
2.7$\,fm, and $\phi/\Xi^-$, $r_c \sim 4.2$\,fm, for the 0-10\% central
collisions. Hadronic transport models including high mass resonance decays
could also describe the ratios. While thermal calculations with GCE work well
for strangeness production in high energy collisions, the change to CE at
$\rm{3\,GeV}$ implies a rather different medium property at high baryon
density.
