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In this VERTICO early science paper we explore in detail how environmental mechanisms, identified in H i , affect the resolved properties of molecular gas reservoirs in cluster galaxies. The molecular gas is probed using ALMA ACA (+TP) observations of ^12 CO(2–1) in 51 spiral galaxies in the Virgo cluster (of which 49 are detected), all of which are included in the VIVA H i survey. The sample spans a stellar mass range of $9\leqslant \mathrm{log}\,{M}_{\star }/{M}_{\odot }\leqslant 11$ . We study molecular gas radial profiles, isodensity radii, and surface densities as a function of galaxy H i deficiency and morphology. There is a weak correlation between global H i and H _2 deficiencies, and resolved properties of molecular gas correlate with H i deficiency: galaxies that have large H i deficiencies have relatively steep and truncated molecular gas radial profiles, which is due to the removal of low-surface-density molecular gas on the outskirts. Therefore, while the environmental mechanisms observed in H i also affect molecular gas reservoirs, there is only a moderate reduction of the total amount of molecular gas.