In the framework of the improved chromomagnetic interaction model, we complete a systematic study of the S-wave tetraquark states   $ Qq\bar{Q}\bar{q} $   (  $ Qq\bar{Q}\bar{q} $  , and   $ Qq\bar{Q}\bar{q} $  ) with different quantum numbers:   $ Qq\bar{Q}\bar{q} $  ,   $ Qq\bar{Q}\bar{q} $  , and   $ Qq\bar{Q}\bar{q} $  . The mass spectra of tetraquark states are predicted, and the possible decay channels are analyzed by considering both the angular momentum and   $ Qq\bar{Q}\bar{q} $  -parity conservation. The recently observed hidden-charm tetraquark states with strangeness, such as   $ Qq\bar{Q}\bar{q} $  ,   $ Qq\bar{Q}\bar{q} $  , and   $ Qq\bar{Q}\bar{q} $  , can be well explained in our model. Additionally, according to the wave function of each tetraquark state, we find that the low-lying states of each   $ Qq\bar{Q}\bar{q} $   configuration have a large overlap to the   $ Qq\bar{Q}\bar{q} $   and   $ Qq\bar{Q}\bar{q} $   meson basis, instead of the   $ Qq\bar{Q}\bar{q} $   and   $ Qq\bar{Q}\bar{q} $   meson basis. This indicates that one can search these tetraquark states in future experiments via the channel of   $ Qq\bar{Q}\bar{q} $   and   $ Qq\bar{Q}\bar{q} $   mesons.