Sheep are one of the most important livestock species in Croatia, found mainly in the Mediterranean coastal and mountainous regions along the East Adriatic coast, well adapted to the environment and mostly kept extensively. Our main objective was therefore to map the positive selection of the X-chromosome (18,983 SNPs that passed quality control), since nothing is known about the adaptation genes on this chromosome for any of the breeds from the Balkan cluster. Analyses were performed on a sample of eight native Croatian breeds (101 females and 100 males) representing the East Adriatic metapopulation and on 10 mouflons (five females and males), all sampled in Croatia. Three classical within-population approaches (extreme Runs of Homozygosity islands, integrated Haplotype Score, and number of Segregating Sites by Length) were applied along with our new approach called Haplotype Richness Drop (HRiD), which uses only the information contained in male haplotypes. We have also shown that phylogenetic analyses, such as the Median-joining network, can provide additional information when performed with the selection signals identified by HRiD. Our new approach identifies positive selection signals by searching for genomic regions that exhibit a sudden decline in haplotype richness. In total, we identified 14 positive selection signals, 11 using the classical approach and three using the HRiD approach, all together containing 34 annotated genes. The most reliable selection signal was mapped by all four approaches in the same region, overlapping between 13.17 and 13.60 Mb, and assigned to the CA5B, ZRSR2, AP1S2, and GRPR genes. High repeatability (86%) of results was observed, as 12 identified selection signals were also confirmed in other studies with sheep. HRiD offers an interesting possibility to be used complementary to other approaches or when only males are genotyped, which is often the case in genomic breeding value estimations. These results highlight the importance of the X-chromosome in the adaptive architecture of domestic ruminants, while our novel HRiD approach opens new possibilities for research.