  The thermoelectric performance at a given output power of a voltage-probe
heat engine, exposed to an external magnetic field, is investigated in linear
irreversible thermodynamics. For the model, asymmetric parameter, general
figures of merit and efficiency at a given output power are analytically
derived. Results show a trade-off between efficiency and output power, and we
recognize optimum-efficiency values at a given output power are enhanced
compared to a B\"uttiker-probe heat engine due to the presence of a
characteristic parameter, namely $d_m$. Moreover, similar to a B\"uttiker-probe
heat engine, the universal bounds on the efficiency are obtained, and the
efficiency at a given output power can exceed the Curzon-Ahlborn limit. These
findings have practical implications for the optimization of realistic heat
engines and refrigerators. By controlling the values of the asymmetric
parameter, the figures of merit, and $d_m$, it may be possible to design more
efficient and powerful thermoelectric devices.
