Thermoelectrics are promising by directly generating electricity from waste heat. However, (sub-) room-temperature thermoelectrics have been a long-standing challenge, due to the vanishing electronic entropy at low temperature. Topological materials offer a new avenue for energy harvesting applications. Recent theories predicted that topological Weyl semimetals (WSMs) at the quantum limit can lead to a non-saturating longitudinal thermopower, as well as a quantized thermoelectric Hall conductivity approaching to a universal value. Here, we experimentally demonstrate the non-saturating thermopower and the signature of quantized thermoelectric Hall conductivity in WSM tantalum phosphide (TaP). An ultrahigh longitudinal thermopower Sxx = 1.1x10^3 muV/K, along with a power factor ~500 muW/cm/K^2, are observed ~40K. Moreover, the thermoelectric Hall conductivity develops a plateau at high-fields and low temperatures, which further collapses onto a single curve determined by universal constants. Our work highlights the unique WSM electronic structure and topological protection of Weyl nodes toward low-temperature energy harvesting applications.