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We investigate the single transverse-spin asymmetry with a $\sin(\phi_h-\phi_S)$ modulation in the charged Kaon produced and in $\Lambda$hyperon produced SIDIS process within the theoretical framework of transversemomentum dependent (TMD) factorization at the next-to-leading-logarithmicorder. The asymmetry is contributed by the convolution of Sivers function andthe unpolarized fragmentation function $D_1$ for the produced hadron. Theparametrization for the proton Qiu-Sterman function, which is closely relatedto the Sivers function, is adopted to numerically estimate the Sivers asymmetryat the kinematical region of Electron Ion Collider (EIC) and Electron IonCollider in China (EicC). The TMD evolution of the TMD parton distributionfunctions are considered by employing the nonperturbative Sudakov form factor.It is found that the predicted Sivers asymmetries $A_{UT}^{\sin(\phi_h-\phi_S)}$ as functions of $x$, $z$ and $P_{hT}$ are sizable at thekinematical configurations of both EIC and EicC. The strange constituent of theproduced charged Kaon and $\Lambda$ hyperon in the final state can be apromising probe of the sea quark Sivers function as well as the flavordependence in the proton target. Therefore, it is important to utilize thefuture EIC facilities to constrain the sea quark distribution functions as wellas the validity of the generalized universality of the Sivers function.

The Sivers asymmetry in charged Kaon and $\Lambda$ hyperon produced SIDIS process at electron ion colliders