The production of D$^{±}$ and $ {D}_s^{\pm } $ charmed mesons is measured using the D$^{±}$/$ {D}_s^{\pm } $→ ϕ(μμ)π$^{±}$ decay channel with 137 fb$^{−1}$ of $ \sqrt{s} $ = 13 TeV proton-proton collision data collected with the ATLAS detector at the Large Hadron Collider during the years 2016–2018. The charmed mesons are reconstructed in the range of transverse momentum 12 < p$_{T}$ < 100 GeV and pseudorapidity |η| < 2.5. The differential cross-sections are measured as a function of transverse momentum and pseudorapidity, respectively, and compared with next-to-leading- order QCD predictions. The predictions are found to be consistent with the measurements in the visible kinematic region within the large theoretical uncertainties.[graphic not available: see fulltext]