  We explore the thermoelectric transport properties of a coexistence
topological semimetal, characterized by the presence of both a pair of Weyl
points and a nodal ring in the quantum limit. This system gives rise to complex
Landau bands when subjected to a magnetic field aligned with the direction
connecting two Weyl points. In the longitudinal configuration, where the
magnetic field is parallel to the electric field or the temperature gradient,
the thermoelectric conductivity indicates a plateau independent of the magnetic
field and the Fermi energy at $\delta$-form short-range scattering. This
platform structure should also exist in pure two-node Weyl semimetals. However,
the thermoelectric conductivity and the Seebeck coefficient are significantly
influenced by the parameters of long-ranged Gaussian or screened Coulomb
scattering potentials for both fixed carrier density and Fermi energy
scenarios. In the transverse configuration, both Gaussian and screened Coulomb
scatterings yield substantial positive magnetoresistance and thermoelectric
conductance. Since the Hall conductivity is larger than the longitudinal one,
the Seebeck coefficient, exhibiting a quadratic increase with the magnetic
field, is close to the dissipationless limit irrespective of scatterings, while
the Nernst response is notably dependent on the scattering mechanism.
Additionally, the model parameter, distinct from the two-node Weyl model,
influences the thermoelectric transport properties. The magnetic field response
of the thermoelectric coefficients to different scattering potentials can be
used as a basis for distinguishing scattering mechanisms in materials.
