Thermoelectrics are promising by directly generating electricity from waste heat. However, (sub-)room-temperature thermoelectrics have been a long-standing challenge due to vanishing electronic entropy at low temperatures. Topological materials offer a new avenue for energy harvesting applications. Recent theories predicted that topological semimetals at the quantum limit can lead to a large, non-saturating thermopower and a quantized thermoelectric Hall conductivity approaching a universal value. Here, we experimentally demonstrate the non-saturating thermopower and quantized thermoelectric Hall effect in the topological Weyl semimetal (WSM) tantalum phosphide (TaP). An ultrahigh longitudinal thermopower Sxx= 1.1x10^3 muV/K and giant power factor ~525 muW/cm/K^2 are observed at ~40K, which is largely attributed to the quantized thermoelectric Hall effect. Our work highlights the unique quantized thermoelectric Hall effect realized in a WSM toward low-temperature energy harvesting applications.