Sterile neutrinos provide active neutrinos with masses and mixing, and hence is one of the well-motivated candidate for dark matter. We discuss the sterile neutrino production mechanisms operating in the early Universe and show that additional scalar coupled to sterile neutrino can significantly change the situation, making moderate sterile-neutrino mixing and small sterile neutrino masses consistent with current cosmological and astrophysical bounds. Further searches for a narrow line in galactic X-rays and even direct searches for keV-scale sterile neutrinos in particle physics experiments can probe the suggested setup.