Quarkyonic matter is expected to play a key role for the transition from hadronic matter to quark matter in compact stars. Within the framework of the relativistic mean-field model and equivparticle model with density-dependent quark masses, we construct the “quark Fermi sea” with a “baryon Fermi surface” to characterize the properties of the quarkyonic matter. In particular, we develop a comprehensive framework to account for the strangeness degrees of freedom, incorporating $\mathrm{\Lambda }$, $\mathrm{\Xi }$, and $\mathrm{\Sigma }$ hyperons as well as strange quarks in a unified quarkyonic framework. Our calculations indicate that the inevitable emergence of hyperons softens the equations of state, leading to a reduction in the equilibrium sound velocity around $n_{\mathrm{b}}\approx 2n_0$, and consequently reducing the masses and radii of neutron stars. When the quark-hadron phase transition is taken into account, the equation of state at high densities exhibits additional softening consistent with current astronomical observational constraints. This softening leads to a maximum equilibrium sound velocity of $v_{eq}^{\max }\approx 0.6c$, which is close to the ultrarelativistic limit of $0.58c$.

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• Nuclear astrophysics
• Nuclear matter in neutron stars
• Nuclear density functional theory