This paper develops a novel cooling and heating system by integrating a novel split thermoelectric cooler (STEC) with photovoltaic power generation and radiative sky cooling. The system uses photovoltaic driven STEC modules to generate cooling and heating combined with radiative sky cooling to improve cooling capacity. By harnessing the distinctive characteristics of photovoltaic technology and radiative sky cooling, the new system is capable of operating continuously for 24 h without requiring any additional energy input. The system mathematical model is established, and the effects of STEC module number, solar illumination intensity, area ratio and ambient temperature on the performance are studied. Results demonstrate that the cooling efficiency of the system is 3.02 and the heating efficiency is 1.86 when the number of STEC modules is 3. In a year, the monthly average heat production of the system fluctuates due to changes in the solar illumination intensity, while the fluctuation of cooling capacity is small. The system cold production is larger than heat production, which is more suitable for application in the area with high demand for year-round refrigeration. The new system has good energy and economic performance with payback time being shorter than that of the photovoltaic-air conditioning system.