Abstarct: The figure of merit of thermoelectric materials, ZT, which determines their efficiency in a thermoelectric device, is low for most bulk materials. Nanoscale materials and structures are one promising way to increase the thermoelectric figure of merit. In this study, the effect of electron scattering on the thermoelectric properties, under quantizing magnetic field, has been investigated. Using the Lippmann-Schwinger equation, the electronic transition coefficients of the studied device were obtained, and finally, using the Landauer-Butticker approach, thermoelectric coefficients were calculated. The system studied in this research is a twodimensional electron gas in the heterogeneous structure of GaAs / AlGaAs with a lateral confinement. The results showed that the increase of the magnetic field, Fermi energy, and phonon mean free path decreased the figure of merit of the studied device but the rise of the temperature increased it.