This thesis investigates the properties of quantum droplets composed of two hyperfine states of potassium-39, confined along one axis, with a focus on the vortices within these droplets. Using Density Functional Theory for mean-field and Lee-Huang-Yang contributions, the extended Gross-Pitaevskii equation was solved in the rotating frame using imaginary time propagation. A key observation is that the angular momentum per particle of the component with a vortex consistently equals 1ℏ, aligning with theoretical predictions. Additionally, stronger confinement (increased squeezing) results in more self-bound configurations. Notably, the system is more self-bound when the vortex is in the less numerous species, compared to when the vortex is in the more numerous component or in both components, which results in the least binding. Squeezing along the z-axis increases the droplet radius in the xy-plane while reducing its thickness in the xz-plane, and interestingly, does not appear to affect the size of the vortex core. These findings suggest that more confined quasi-2D systems could provide experimentally feasible setups for studying vortices.