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The production of K∗(892)0 and ϕ(1020) resonances has been measured in p-Pb collisions at sNN−−−√ = 8.16 TeV using the ALICE detector. Resonances are reconstructed via their hadronic decay channels in the rapidity interval −0.5 < y < 0 and the transverse momentum spectra are measured for various multiplicity classes up to pT = 20 GeV/c for K∗(892)0 and pT = 16 GeV/c for ϕ(1020). The pT -integrated yields and mean transverse momenta are reported and compared with previous results in pp, p-Pb and Pb-Pb collisions. The xT scaling for K∗(892)0 and ϕ(1020) resonance production is newly tested in p-Pb collisions and found to hold in the high-pT region at Large Hadron Collider energies. The nuclear modification factors (RpPb) as a function of pT for K∗0 and ϕ at sNN−−−−√ = 8.16 TeV are presented along with the new RpPb measurements of K∗0, ϕ , Ξ, and Ω at sNN−−−√ = 5.02 TeV. At intermediate pT (2-8 GeV/c), RpPb of Ξ, Ω show a Cronin-like enhancement, while K∗0 and ϕ show no or little nuclear modification. At high pT (> 8 GeV/c), the RpPb values of all hadrons are consistent with unity within uncertainties. The RpPb of K∗(892)0 and ϕ(1020) at sNN−−−√ = 8.16 and 5.02 TeV show no significant energy dependence.