We propose a thermoelectric cooling device based on an atomic-sized junction. Using first-principles approaches, we investigate the working conditions and the coefficient of performance (COP) of an atomic-scale electronic refrigerator where the effects of the phonon's thermal current and local heating are included. It is observed that the functioning of the thermoelectric nanorefrigerator is restricted to a narrow range of driving voltages. Compared with the bulk thermoelectric system with the overwhelmingly irreversible Joule heating, the 4-Al atomic refrigerator has a higher efficiency than a bulk thermoelectric refrigerator with the same thermoelectric figure of merit (ZT) due to suppressed local heating via the quasi-ballistic electron transport and small driving voltages. Quantum nature due to the size minimization offered by atomic-level control of properties facilitates electron cooling beyond the expectation of the conventional thermoelectric device theory.