Abstract: The mass spectra of hidden heavy-flavored tetraquark systems with strange quarks, q\barsQ\barQ and s\barsQ\barQ, are calculated based on the Hadro-quarkonium (H-Q) model and the bag model that includes chromomagnetic interaction (CMI). The results from the H-Q model indicate that when the heavy quarkonium Q\barQ is in an excited state, the binding energy between the strange meson and Q\barQ is significant, potentially forming a compact structure. Therefore, it is possible to identify such structures experimentally through the decay process from the excited state of Q\barQ to the ground state. Additionally, we discuss the mass spectra of q\barsQ\barQ and s\barsQ\barQ using the CMI bag model: the mass spectrum of q\barsQ\barQ differs from the experimentally observed \rmZ_\rmcs^(4000) and \rmZ_\rmcs^(4220) by only about 20 MeV. The mass calculation results for s\barsQ\barQ are in good agreement with some experimental findings. Based on this, we support the idea that exotic tetraquark states with strange quarks may exhibit more compact structures.