  For the fractional quantum Hall states on a finite disc, we study the
thermoelectric transport properties under the influence of an edge and its
reconstruction. In a recent study on a torus [Phys. Rev. B 101, 241101 (2020)],
Sheng and Fu found a universal non-Fermi liquid power-law scaling of the
thermoelectric conductivity $\alpha_{xy} \propto T^{\eta}$ for the gapless
composite Fermi-liquid state. The exponent $\eta \sim 0.5$ appears an
independence of the filling factors and the details of the interactions. In the
presence of an edge, we find the properties of the edge spectrum dominants the
low-temperature behaviors and breaks the universal scaling law of the
thermoelectric conductivity. In order to consider individually the effects of
the edge states, the entanglement spectrum in real space is employed and tuned
by varying the area of subsystem. In non-Abelian Moore-Read state, the Majorana
neutral edge mode is found to have more significant effect than that of the
charge mode in the low temperature.
