In spite of an enormous progress of standard ΛCDM cosmology (SC) a number of alternative approaches has been suggested because there are great puzzles with an origin and essence of dark matter and dark energy which unavoidably arise in the framework of the standard approach. Alternative approaches have to pass a number of observational tests including one with distant type Ia supernovae (SNe Ia) data. As it was shown [1] a conformal cosmological (CC) approach can explain cosmological SNe Ia data without introducing Λ-term, however, introducing an exotic rigid equation of state is needed. Later on, these statements were confirmed with larger samples of observational data [2, 3]. In the paper we check previous claims with joint SDSS-II and SNLS supernova samples.