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The inclusive production of the charm-strange baryon Ω0c is measured for the first time via its hadronic decay into Ω−π+ at midrapidity (|y|<0.5) in proton-proton (pp) collisions at the centre-of-mass energy s√=13 TeV with the ALICE detector at the LHC. The transverse momentum (pT) differential cross section multiplied by the branching ratio is presented in the interval 2<pT<12 GeV/c. The pT dependence of the Ω0c-baryon production relative to the prompt D0-meson and to the prompt Ξ0c-baryon production is compared to various models that take different hadronisation mechanisms into consideration. In the measured pT interval, the ratio of the pT-integrated cross sections of Ω0c and prompt Λ+c baryons multiplied by the Ω−π+ branching ratio is found to be larger by a factor of about 20 with a significance of about 4σ when compared to e+e− collisions.