This paper reports a summary of searches for a fermionic dark matter candidate in the context of theoretical models characterised by a mediator particle exchange in the s-channel. The data sample considered consists of pp collisions delivered by the Large Hadron Collider during its Run 2 at a centre-of-mass energy of $\sqrt{s} = 13\,\textrm{TeV}$ and recorded by the ATLAS detector, corresponding to up to 140 fb$^{-1}$. The interpretations of the results are based on simplified models where the new mediator particles can be spin-0, with scalar or pseudo-scalar couplings to fermions, or spin-1, with vector or axial-vector couplings to fermions. Exclusion limits are obtained from various searches characterised by final states with resonant production of Standard Model particles, or production of Standard Model particles in association with large missing transverse momentum.