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A<sc>bstract</sc> We report the first measurement of the inclusivee+e−→$$ b\overline{b} $$ →$$ {D}_s^{\pm } $$ Xande+e−→$$ b\overline{b} $$ → D0/$$ {\overline{D}}^0 $$ Xcross sections in the energy range from 10.63 to 11.02 GeV. Based on these results, we determineσ(e+e−→$$ {B}_s^0{\overline{B}}_s^0 $$ X) andσ(e+e−→$$ B\overline{B} $$ X) in the same energy range. We measure the fraction of$$ {B}_s^0 $$ events at Υ(10860) to befs= ($$ {22.0}_{-2.1}^{+2.0} $$ )%. We determine also the ratio of the$$ {B}_s^0 $$ inclusive branching fractions$$ \mathcal{B} $$ ($$ {B}_s^0 $$ → D0/$$ {\overline{D}}^0 $$ X)/$$ \mathcal{B} $$ ($$ {B}_s^0 $$ →$$ {D}_s^{\pm } $$ X) = 0.416 ± 0.018 ± 0.092. The results are obtained using the data collected with the Belle detector at the KEKB asymmetric-energye+e−collider.more » « less