We investigate how hypothetical particles-sterile neutrinos-can be produced in the interior of exploding supernovae via the resonant conversion of nu over bar mu and nu over bar tau. The novelty of our treatment lies in the proper account of the resulting lepton number diffusion. We compute the yield of sterile neutrinos and find that even after taking into account backreaction, sterile neutrinos can carry out a sizeable fraction of the total energy of the explosion comparable to that of active neutrinos. The production is, however, sensitive to the temperature in the inner supernovae regions, making robust predictions of challenging. In order to understand whether this production affects supernova evolution and can therefore be constrained, detailed simulations including the effects of sterile neutrinos are needed.