We have studied fluxoid quantization effects in mesoscopic Al samples consisting of a small number of square loops. In short microladders a pronounced substructure of the Little-Parks oscillations (i.e. the oscillations of the critical temperature T-c as a function of the applied magnetic flux Phi) has been found. These new features in T-c(Phi) originate from transitions between different quantum states, each having a specific order parameter profile and how pattern of the supercurrents. The experimental data are in excellent agreement with the T-c(Phi) calculated within the de Gennes-Alexander model for superconducting micronetworks.