A search for double-heavy tetraquark state candidates Xccsˉsˉ decaying to Ds+Ds+ and Ds∗+Ds∗+ is presented for the first time using the data samples of 102 million Υ(1S) and 158 million Υ(2S) events, and the data samples at s = 10.52~GeV, 10.58~GeV, and 10.867~GeV corresponding to integrated luminosities of 89.5~fb−1, 711.0~fb−1, and 121.4~fb−1, respectively, accumulated with the Belle detector at the KEKB asymmetric energy electron-positron collider. The invariant-mass spectra of the Ds+Ds+ and Ds∗+Ds∗+ are studied to search for possible resonances. No significant signals are observed, and the 90% confidence level upper limits on the product branching fractions [B(Υ(1S,2S)→Xccsˉsˉ+anything)×B(Xccsˉsˉ→Ds+Ds+(Ds∗+Ds∗+))] in Υ(1S,2S) inclusive decays and the product values of Born cross section and branching fraction [σ(e+e−→Xccsˉsˉ+anything)×B(Xccsˉsˉ→Ds+Ds+(Ds∗+Ds∗+))] in e+e− collisions at s = 10.52~GeV, 10.58~GeV, and 10.867~GeV under different assumptions of Xccsˉsˉ masses and widths are obtained