The detection of a sterile neutrino could constitute the first observation of a particle that could have been produced before Big-Bang Nucleosynthesis (BBN), and could provide information about the yet untested pre-BBN era. The cosmological evolution in this era could be drastically different than typically assumed, in what constitutes the standard cosmology, as happens in a variety of motivated particle models. In this work we assess the sensitivity to different pre-BBN cosmologies in which entropy is conserved of 0.01 eV to 1 MeV mass sterile neutrinos produced in the early Universe via resonant active-sterile oscillations, which requires a large lepton asymmetry. We identify mass ranges where it is possible to have two populations of the same sterile neutrino, one with a colder and one with a hotter momentum spectra, which is in principle an observable effect. Furthermore, we show the regions in mass and mixing where fully resonant production (i.e. simultaneously coherent and adiabatic) can occur. We find that in all the cosmologies we consider, including the standard one, fully resonantly produced sterile neutrinos in the eV-mass range can evade all cosmological constraints.In the absence of a large lepton asymmetry the oscillations are non-resonant and sterile neutrinos are produced via the Dodelson-Widrow (DW) mechanism [45]. In the standard cosmology this mechanism results in a Fermi-Dirac relic momentum distribution of sterile neutrinos, with a reduced magnitude with respect to active neutrinos. Several studies have already been carried out on non-resonantly produced sterile neutrinos in different pre-BBN cosmologies ). This work is complementary to these previous studies in that we concentrate on the production of sterile neutrinos via resonant active-sterile oscillations, an often considered production mechanism that requires a significant lepton asymmetry in active neutrinos (this is the Shi-Fuller mechanism [52], see also Ref. [53,54]). In this case, sterile neutrinos are produced with a colder momentum distribution (i.e. with a lower average momentum) that is different from a Fermi-Dirac spectrum, even in the standard cosmology. In particular, we study the effect of different cosmologies on resonantly produced sterile neutrinos with mass 10 −2 eV < m s < 1 MeV. Since the production rate is usually not fast enough for sterile neutrinos to equilibrate, the final relic abundance and spectrum are fixed by freeze-in.We will analyze resonant sterile neutrino production within several example cosmological models in which entropy is conserved, characterized by the magnitude and temperature dependence of the Hubble expansion rate H in the non-standard cosmological phase. If H is larger than it would be in the standard cosmology, the resonant production of sterile neutrinos during this phase is suppressed with respect to standard production, and if H is lower, the production is enhanced. If the production is fully resonant, which requires adiabaticity and coherence at the resonance, the relic sterile neutrino ...