A search for weakly interacting massive dark-matter particles produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and missing transverse momentum are considered. The analysis uses $36.1 \, \mathrm {fb}^{-1}$ of proton?proton collision data recorded by the ATLAS experiment at $\sqrt{s}=13$ ?TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are interpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour-neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50?GeV are excluded assuming a dark-matter candidate mass of 1?GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross-section of 300 times the predicted rate for mediators with masses between 10 and $50\, \hbox {GeV}$ and assuming a dark-matter mass of $1 \,\hbox {GeV}$ and unitary coupling. Constraints on colour-charged scalar simplified models are also presented. Assuming a dark-matter particle mass of $35\, \hbox {GeV}$ , mediator particles with mass below $1.1\, \hbox {TeV}$ are excluded for couplings yielding a dark-matter relic density consistent with
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