The spider genus Dysdera has undergone a remarkable diversification in the oceanic archipelago of the Canary Islands, ~60 endemic species originated during the 20 million years since the origin of the archipelago. This evolutionary radiation has been accompanied by substantial dietary shifts, often characterized by phenotypic modifications encompassing morphological, metabolic and behavioral changes. Hence, these endemic spiders represent an excellent model for understanding the evolutionary drivers and to pinpoint the genomic determinants underlying adaptive radiations. Recently, we achieved the first chromosome-level genome assembly of one of the endemic species, D. silvatica, providing a high-quality reference sequence for evolutionary genomics studies. Here, we conducted a low-coverage based resequencing study of a natural population of D. silvatica from La Gomera island. Taking advantage of the new high-quality genome, we characterized genome-wide levels of nucleotide polymorphism, divergence, and linkage disequilibrium, and inferred the demographic history of this population. We also performed comprehensive genome-wide scans for recent positive selection. Our findings uncovered exceptionally high levels of nucleotide diversity and recombination in this geographically restricted endemic species, indicative of large historical effective population sizes. Furthermore, we identified genomic regions potentially under positive selection, shedding light on relevant biological processes, such as vision and nitrogen extraction as possible targets of adaptation and eventually, as drivers of the species diversification. This pioneering study in spiders endemic of an oceanic archipelago lays the groundwork for broader population genomics investigations aimed at understanding the genetic mechanisms driven adaptive radiations in island ecosystems.