We investigate the hybrid compact stars consisting of nucleons, hyperons and three flavor color-flavor-locked quark phase under global neutrality and chemical equilibrium conditions. The hadronic equations of state are computed within the framework of energy density functionals based on the relativistic mean field theory by employing two different model. The quark matter phase of equation of state is computed by using Quark Quasiparticle model derived from a non-relativistic energy density-functional approach. A set of hybrid equations of state for superdense hadron-quark matter is obtained and, employed to investigate the structural properties of non-rotating and rotating compact stars. The internal structure of rotating star with observed spin down frequencies, exhibiting shrinkage of soft quark core of compact stars are discussed for constant baryonic mass. We present the theoretically computed limits of radii for the spin down configurations of hybrid stars corresponding to the recently observed millisecond pulsars. The various EOSs considered in the present work are well within the recent astrophysical constraints on mass and radius measurements (Riley et al. in Astrophys J Lett 918(2):L27, 2021; Millet et al. in http://arxiv.org/abs/2105.06979, 2021) and dimensionless tidal deformability (Λ1.4\documentclass[12pt]{minimal}
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\begin{document}$$\varLambda _{1.4}$$\end{document}) (Abbott et al. in Phys Rev Lett 121(16):161101, 2018; Li et al. in Eur Phys J A 57(1):1–10, 2021).
