We investigate the cosmological consequences of light sterile neutrinos with altered dispersion relations (ADRs) and couplings to an ultra-light, axion-like scalar field. In particular we study the impact on the number of additional, light, fermionic degrees of freedom and primordial nucleosynthesis. While the ADR leads to a new potential term in the Hamiltonian, the coupling to the scalar field results in a time dependent, effective mass contribution. We solve the quantum kinetic equations (QKEs) for the neutrino density matrix and find that in certain parameter regions both new physics effects can individually yield a suppressed population of sterile neutrino species and the correct observed amount of helium in nucleosynthesis. Combining both effects opens up new patches of parameter space excluded by experimental bounds applying to models featuring only one of the effects.