To fully exploit inlet sunlight, a novel hybrid system comprising a concentrated photovoltaic cell, a thermoelectric generator, and a thermoelectric cooler is established. The thermoelectric generator generates electricity by thermally harnessing the solar spectrum energy unavailable to the concentrated photovoltaic cell and then drives the thermoelectric cooler to produce additional cooling. With full consideration of internal and external irreversibility, the numerical model of the hybrid system is developed, where comprehensive heat transfer equations are constructed by the effectiveness-number of transfer units method. Subsequently, the performance characteristics of the system are evaluated by energetic and exergetic analysis. Over the operating range of the thermoelectric unit, when the performance enhancement of the hybrid system is maximized, the associated power density, energy efficiency, and exergy efficiency are, respectively, 42.828 Wm-2, 0.0251, and 0.0255, which are improved by 3.53%, 3.72%, and 3.66% in comparison to the stand-alone concentrated photovoltaic system. Meanwhile, the exergy destruction rate density is reduced by 0.49%. Furthermore, comprehensive sensitivity analyses are undertaken to derive the effects of critical designing parameters and operating conditions on the overall performance. The obtained outcomes may contribute to the design and operation of such a cogeneration system.