The production of top quark pairs in association with heavy-flavour jets ($b/c$) is a difficult process to calculate and model, and is one of the leading sources of background affecting the measurement of processes such as the associated production of a Higgs boson and a top-quark pair, $t\bar{t}H$. To improve our understanding of this process, a new inclusive and differential measurement of the production of $t\bar{t}$ accompanied by a jet initiated by $b$ quarks. The results presented were achieved using the full LHC Run-2 dataset collected by ATLAS.