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The blue skate (Dipturus batis) has a patchy distribution across the North‐East Atlantic Ocean, largely restricted to occidental seas around the British Isles following fisheries‐induced population declines and extirpations. The viability of remnant populations remains uncertain and could be impacted by continued fishing and by‐catch pressure, and the projected impacts of climate change. We genotyped 503 samples of D. batis, obtained opportunistically from the widest available geographic range, across 6 350 single nucleotide polymorphisms (SNPs) using a reduced‐representation sequencing approach. Genotypes were used to assess the species' contemporary population structure, estimate effective population sizes and identify putative signals of selection in relation to environmental variables using a seascape genomics approach. We identified genetic discontinuities between inshore (British Isles) and offshore (Rockall and Faroe Island) populations, with differentiation most pronounced across the deep waters of the Rockall Trough. Effective population sizes were largest in the Celtic Sea and Rockall, but low enough to be of potential conservation concern among Scottish and Faroese sites. Among the 21 candidate SNPs under positive selection was one significantly correlated with environmental variables predicted to be affected by climate change, including bottom temperature, salinity and pH. The paucity of well‐annotated elasmobranch genomes precluded us from identifying a putative function for this SNP. Nevertheless, our findings suggest that climate change could inflict a strong selective force upon remnant populations of D. batis, further constraining its already‐restricted habitat. Furthermore, the results provide fundamental insights on the distribution, behaviour and evolutionary biology of D. batis in the North‐East Atlantic that will be useful for the establishment of conservation actions for this and other critically endangered elasmobranchs. [ABSTRACT FROM AUTHOR]