The aim of this study is to assess the storability and nutritional value of new Polish apple cultivars recommended for cultivation after storage under low-oxygen atmospheric conditions (ULO and DCA). Fruit characteristics of ‘Chopin’ and clone ‘JB’ were evaluated in relation to commonly grown apple cultivars. Fruits of six selected apple cultivars were stored for a period of 9 months in conventional (0.04% CO2: 21% O2), Ultra-Low Oxygen (1.5% CO2: 1.5% O2), and Dynamic Controlled Atmosphere (0.6% CO2: 0.6% O2) cold storage. Physicochemical characteristics of the apples (firmness, soluble solids, acidity, and fibre content), nutritional and antioxidant values of the fruit (P, K, Ca, Mg, Fe, Cu, Zn, total polyphenols, total flavonoids, and antioxidant capacity), and safety of consumption (residues of pesticides) were assessed. The new cultivar ‘Chopin’ and clone ‘JB’ were characterised by above-average acidity and clone ‘JB’ stood out in terms of antioxidant properties. Storage in a low-oxygen atmosphere in DCA was more effective in limiting fruit ripening than conventional cold storage, contributing to the preservation of the high potential of biologically active compounds in the apples. Apples after 9 months of storage were characterised by higher firmness (from 3.5 to 14 N), higher total polyphenol content in the flesh (from 8 to 23 mg∙100 g−1 FW) and peel (from 32 to 97 mg∙100 g−1 FW), as well as higher antioxidant capacity in the flesh (from 15 to 37 mg AAE∙100 g−1 FW) and peel (from 28 to 59 mg AAE∙100 g−1 FW) when stored in DCA compared to cold storage.