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We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, 𝑎 HVP 𝜇 , in the so-called short and intermediate time-distance windows, 𝑎 SD 𝜇 and 𝑎 W 𝜇 . We employ gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with 𝑁 𝑓 = 2 + 1 + 1 flavours of Wilson-clover twisted-mass quarks with masses of all the dynamical quark flavours tuned close to their physical values. The simulations are carried out at three values of the lattice spacing equal to ≃ 0.057, 0.068 and 0.080 fm with spatial lattice sizes up to 𝐿 ≃ 7.6 fm. For the short distance window we obtain 𝑎 SD 𝜇 = 69.27 (34) • 10 −10 , in agreement with the dispersive determination based on experimental 𝑒 + 𝑒 − data. For the intermediate window we get instead 𝑎 W 𝜇 = 236.3 (1.3) • 10 −10 , which is consistent with recent determinations by other lattice collaborations, but disagrees with the dispersive determination at the level of 3.6 𝜎.