The increasing use of electronic devices has raised expectations in how we communicate and share data, particularly in critical scenarios such as natural disasters or human negligence that severely affect existing infrastructure. Unmanned aerial vehicles (UAVs) used as Drone Base Stations (DBS), offer an innovative solution by providing wireless connectivity over cellular networks and distributing critical items to users in areas with limited coverage. This paper proposes three novel models based on the classic p-median problem to solve the optimal candidate site drone localization problem in time. More precisely, in our models, we introduce the time dimension of how drones move during time slots, which determines their performance. Additionally, we incorporate a mechanism that allows drones to move in a more free or restricted mode following their predefined label numbers. Finally, in the objective functions, we consider the cost of moving drones plus the user connectivity costs versus the cost of connecting users only. In our experimental setup, we compare all our models and determine differences in terms of CPU times, obtained objective function values, drone strategy, and associated costs.