Potato virus A (PVA) and potato virus Y (PVY) are two members of genus Potyvirus infecting potato crops worldwide. Host resistance offers an economical and effective means for the control or management of these viruses. In this study, 20 potato clones were screened for their resistance against PVA and PVY by mechanical or graft inoculation assay, and were explored for the relationship between extreme resistance genes Ra and Ry by the detection of molecular markers linked to Ry, Ry, and Ry. Six clones, including Barbara, Jizhangshu 8, Longshu 7, Longshu 8, M6, and Solara, were found to be extremely resistant to both PVA and PVY; three clones (AC142, Eshu 3, and Shepody) were deemed to be extremely resistant to PVA but susceptible to PVY. To further reveal the inheritance of the extreme resistance (ER) against PVA, a tetraploid F1 population of Barbara × F58050 (susceptible to both PVY and PVA) and a tetraploid BC1 population of BF145 (a PVA-resistant but PVY-susceptible progeny of Barbara × F58050) × F58050 were obtained. Phenotyping of the F1 and BC1 populations by graft inoculation with PVA showed segregation ratios of 3:1 and 1:1 (resistant:susceptible), respectively. These results suggest that two independent loci control ER against PVA in Barbara: one confers ER to both PVA and PVY and the other confers ER to PVA only. The deduced genotype of Barbara is RyryryryRararara.