The production of a W boson in association with a single charm quark is studied using140 fb−1 of √s = 13 TeV proton–proton collision data collected with the ATLAS detector at the Large Hadron Collider. The charm quark is tagged by the presence of a charmed hadron, reconstructed with a secondary-vertex fit. The W boson is reconstructed from the decay to either an electron or a muon and the missing transverse momentum present in the event. The W + D(∗) process is sensitive to the strange quark PDF, and can be combined with other measurements to improve uncertainties and central values of global PDF fits. Charmed mesons are reconstructed in the decay channels D+ → K−π+π+, D∗+ → D0π+ → (K−π+)π+, D+ → φπ → (KK)π, and Ds → φπ → (KK)π and the charge conjugate decays in the fiducial regions where pT(e, μ) > 30 GeV , |η(e, μ)| < 2.5, pT(D(∗)) > 8 GeV , and |η(D(∗))| < 2.2. The integrated and normalized differential cross-sections as a function of the pseudorapidity of the lepton from the W boson decay, and of the transverse momentum of the charmed hadron, are extracted for the D+ → Kππ and D∗ → D0π → Kππ decay modes. The total fiducial cross section is measured for the Ds → φπ → (KK)π and D+ → φπ → (KK)π decay modes. All observables are extracted from the data using a profile likelihood fit. The measured total fiducial cross-sections for the D+ → Kππ and D∗ → D0π → Kππ modes are σ(OS−SS, fid) (W −+D+) = 50.2 ± 0.2 (stat.) +2.4−2.3 (syst.) pb, σ (OS−SS, fid) (W ++D−) = 48.5 ± 0.2 (stat.) +2.3−2.2 (syst.) pb, σ(OS−SS, fid) (W −+D∗+) = 51.1 ± 0.4 (stat.) +1.9−1.8 (syst.) pb, and σ(OS−SS, fid) (W ++D∗−) = 50.0 ± 0.4 (stat.) +1.9−1.8 (syst.) pb. These differential and total cross section results are compared with the predictions of next-to-leading-order quantum chromodynamics calculations performed using state-of-the-art parton distribution functions. Additionally, the ratio of charm to anti-charm production cross-sections is studied to probe the s- ̄s quark asymmetry. The ratio is found to be Rc = 0.971 ± 0.006 (stat.) ± 0.011 (syst.). The ratio and cross-section measurements are consistent with the predictions obtained with parton distribution function sets that have a symmetric s- ̄s sea, indicating that any s- ̄s asymmetry in the Bjorken-x region relevant for this measurement is small. For the Ds → φπ → (KK)π and D+ → φπ → (KK)π analysis, the observables that are measured are the inclusive cross section in both charges for the W +Ds process, the ratio of the cross sections with respect to the charge, and the ratio of the Ds to the D+ process. The measured values are σ(OS−SS, fid) (W −+D+s ) =17.8±0.4 (stat.) +1.8−1.6 (syst.) pb, σ(OS−SS, fid) (W ++D−s ) = 15.8±0.4 (stat.) +1.5−1.4 (syst.) pb, Rc (Ds) =0.885 ± 0.029 (stat.)+0.059−0.057 (syst.), and R(D+/Ds) = 2.93 ± 0.06(stat.) ± 0.24 (sys.). These result are consistent with the differential W + D+ analysis within 1.5 standard deviations, and are at a lower precision due to lower data and MC simulation statistics and increased systematic uncertainties related to background modeling.