Leptin-associated genetic variants were positively associated with COVID-19 severity (OR = 1.289; 95% CI: 1.0766–1.501, p = 1.92 × 10−2), whilst no statistically significant evidence was found between SNPs for JAK2 (OR = 1.006; 95% CI: 0.950–1.061, p = 0.83) and lymphocyte percentage (OR = 0.989; 95% CI: 0.908–1.069, p = 0.78) with COVID-19 severity. This evidence concerns the gene JAK2 and COVID-19.