occurring at the upper critical field Hc2, is demonstrated from the �(T) � T near Hc2 and �(T) � T 2 when further increasing field. Large residual linear term �0/T at zero field and the rapid increase of �(H)/T at low field indicate that the superconducting gap in Ce2PdIn8 has nodes, likely d-wave symmetry. The sharp jump of �(H)/T near Hc2 gives evidence for a first-order phase transition at low temperature. These results suggest the existence of a low-temperature-high-field Q phase in Ce2PdIn8, where magnetic order is directly coupled to d-wave superconductivity, as in CeCoIn5.