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The transverse momentum (pT) differential production cross section of the promptly-produced charm-strange baryon Ξ0c (and its charge conjugate Ξ0c¯¯¯¯¯¯) is measured at midrapidity via its hadronic decay into π+Ξ− in p−Pb collisions at a centre-of-mass energy per nucleon−nucleon collision sNN−−−√ = 5.02 TeV with the ALICE detector at the LHC. The Ξ0c nuclear modification factor (RpPb), calculated from the cross sections in pp and p−Pb collisions, is presented and compared with the RpPb of Λ+c baryons. The ratios between the pT-differential production cross section of Ξ0c baryons and those of D0 mesons and Λ+c baryons are also reported and compared with results at forward and backward rapidity from the LHCb Collaboration. The measurements of the production cross section of prompt Ξ0c baryons are compared with a model based on perturbative QCD calculations of charm-quark production cross sections, which includes only cold nuclear matter effects in p−Pb collisions, and underestimates the measurement by a factor of about 50. This discrepancy is reduced when the data is compared with a model in which hadronisation is implemented via quark coalescence. The pT-integrated cross section of prompt Ξ0c-baryon production at midrapidity extrapolated down to pT = 0 is also reported. These measurements offer insights and constraints for theoretical calculations of the hadronisation process. Additionally, they provide inputs for the calculation of the charm production cross section in p−Pb collisions at midrapidity.