Multigap superconductivity modulated by quantum confinement effects in a superlattice of quantum wells is presented. Our theoretical BCS approach captures the low-energy physics of a shape resonance in the superconducting gaps when the chemical potential is tuned near a Lifshitz transition. We focus on the case of weak Cooper pairing coupling channels and strong pair exchange interaction driven by repulsive Coulomb interaction that allows us to use the BCS theory in the weak-coupling regime neglecting retardation effects, like in quantum condensates of ultracold gases. The calculated matrix element effects in the pairing interaction are shown to yield a complex physics near the particular quantum critical points due to Lifshitz transitions in multigap superconductivity. Strong deviations of the ratio 2Δ/T c from the standard BCS value as a function of the position of the chemical potential relative to the Lifshitz …