Multi-valued logic has been a significant focus of research in various fields with the advancement of information technology. One approach to realizing ternary logic is integrating of a threshold switching (TS) device with a transistor, but this method often entails a complex fabrication process. This work suggests a ternary gate-connected threshold switching thin-film transistor (TS-TFT) by serially connecting the TS device with a bottom-gate thin-film transistor (TFT). The fabrication process is simplified with a structure that shares electrodes and insulators. Different threshold voltages from TS and TFT devices produce stable multiple states. The Pt/HfO2/TiN TS device has an electronic trapping/detrapping switching mechanism that exhibits low power consumption and high reliability. With the superior electrical performance of an amorphous indium gallium zinc oxide TFT, the TS-TFT has stable endurance. Furthermore, pulse switching and ternary inverter are demonstrated from the practical point of view.