A new cultivar of apple tree, ‘MINNB42’, that is characterized by its fruit that is distinct in its ability to develop deeply colored red fruit skin in climates (such as southern Pennsylvania and southern New York) that are not conducive to producing well-colored ‘Honeycrisp’ fruit, its fruit with a diameter of 7 to 8.4 cm, its fruit with a texture that is very crisp when eaten, its fruit with skin that is relatively thin and easy to penetrate when eaten, its fruit with a flavor that is sub-acid, its moderate tree growth rate, and its cold hardness in U.S.D.A. Zone 4.