The disk midplane temperature is potentially affected by the dust traps/rings. The dust depletion beyond the water snowline will cast a shadow. In this study, we adopt a detailed gas-grain chemical reaction network, and investigate the radial gas and ice abundance distributions of dominant carbon-, oxygen-, and nitrogen-bearing molecules in disks with shadow structures beyond the water snowline around a proto-solar-like star. In shadowed disks, the dust grains at r ∼ 3–8 au are predicted to have more than ∼5–10 times the amount of ices of organic molecules such as H2CO, CH3OH, and NH2CHO, saturated hydrocarbon ices such as CH4 and C2H6, in addition to H2O, CO, CO2, NH3, N2, and HCN ices, compared with those in non-shadowed disks. In the shadowed regions, we find that hydrogenation (especially of CO ice) is the dominant formation mechanism of complex organic molecules. The gas-phase N/O ratios show much larger spatial variations than the gas-phase C/O ratios; thus, the N/O ratio is predicted to be a useful tracer of the shadowed region. N2H+ line emission is a potential tracer of the shadowed region. We conclude that a shadowed region allows for the recondensation of key volatiles onto dust grains, provides a region of chemical enrichment of ices that is much closer to the star than within a non-shadowed disk, and may explain to some degree the trapping of O2 ice in dust grains that formed comet 67P/Churyumov-Gerasimenko. We discuss that, if formed in a shadowed disk, Jupiter does not need to have migrated vast distances.