We investigate electric and magnetic properties of quasi-one-dimensional transition-metal carbides Sc3TC4 (T = Co, Ru, and Os), and their mixed crystals Sc3(Co1-xRux)C4 and Sc3(Ru1-xOsx)C4. Sc3CoC4 exhibits successive phase transitions of charge-density-wave transition at TCDW ~ 140 K, Peierls-like structural transition at Ts ~ 70 K, and superconducting transition at Tc ~ 5 K. Sc3RuC4 and Sc3OsC4 exhibit a phase transition at T* ~ 220 K and 250 K, respectively, which should occur in the low-dimensional electronic structure. For Sc3CoC4, it is revealed by the investigation of the electric and magnetic properties of Sc3(Co1-xRux)C4 that the phase transitions at TCDW, Ts, and Tc exhibit different robustness against Ru doping. For Sc3RuC4 and Sc3OsC4, it is revealed by the investigation of the electric and magnetic properties of Sc3(Ru1-xOsx)C4 that an identical kind of phase transition occurs at T*. Additionally, the present study reveals that the phase transition at T* in Sc3RuC4 and Sc3OsC4 is inherently different from the phase transitions at TCDW, Ts, and Tc in Sc3CoC4.