The result of a search for the production of the supersymmetric partner of the bottom-quark ($\tilde{b}_{1}$) using 79.8\,\mathrm{fb}^{-1} of data collected at \sqrt{s} = 13\,\mathrm{TeV} by the ATLAS detector in Run 2 is reported. In the supersymmetric scenarios considered the bottom-squarks decay to a $b$-quark and the second lightest neutralino, $\tilde{b}_{1} \rightarrow b + \tilde{\chi}^{0}_{2}$. The $\tilde{\chi}^{0}_{2}$ is assumed to subsequently decay with $100\%$ branching ratio to the Standard-Model-like Higgs boson ($h$) and the lightest neutralino: $\tilde{\chi}^{0}_{2} \rightarrow h + \tilde{\chi}^{0}_{1}$. The $\tilde{\chi}^{0}_{1}$ is assumed to be the lightest supersymmetric particle (LSP) and is stable. Two signal mass configurations are targeted: the first has a constant LSP mass of 60\,\mathrm{GeV}; and the second has a constant mass difference between the $\tilde{\chi}^{0}_{2}$ and $\tilde{\chi}^{0}_{1}$ of 130\,\mathrm{GeV}. The final states considered contain zero leptons, three or more $b$-jets, and large missing transverse momentum. No significant excess of events over the Standard Model background expectation is observed in any of the signal regions considered. Limits at the $95\%$ confidence level are placed in the simplified models considered, and bottom-squarks with mass up to 1400\,\mathrm{GeV} are excluded.

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