We report a search for a heavier partner of the recently observed Zcs
(3985)
−
state, denoted as Z’cs
−
, in the process e+e−→K+Ds
∗−D∗0+c.c., based on e+e−
collision data collected at the center-of-mass energies of √s = 4.661, 4.682 and 4.699 GeV with the BESIII detector. The Z’cs
−
is of interest as it is expected to be a candidate for a hidden-charm and open-strange tetraquark. A partial-reconstruction technique is used to isolate K+
recoil-mass spectra, which are probed for a potential contribution from Z’cs
−→Ds
∗−D∗0
(c.c.). We find an excess of Z’cs
−→Ds
∗−D∗0
(c.c.) candidates with a significance of 2.9σ, after considering systematic uncertainties, at a mass of (4123.5 ± 0.7stat. ± 1.1syst.) MeV/c
2. As the data set is limited in size, the upper limits are evaluated at the 90% confidence level on the product of the Born cross section and the branching fraction of Z’cs
−→Ds
∗−D∗0
, σBorn·B at the three energy points, under different assumptions of the Z’cs
−
mass from 4.120 to 4.140 MeV and of the width from 10 to 50 MeV. Under various mass and width assumptions, the upper limits of σBorn·B are found to lie in the range of 2∼6, 3∼7 and 3∼6 pb at √s = 4.661, 4.682 and 4.699 GeV, respectively. The larger data samples that will be collected in the coming years will allow a clearer picture to emerge concerning the existence and nature of the Z’cs
−
state. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.