Given billboard and trajectory database, finding a limited number of billboard slots for maximizing the influence is an important problem in the context of billboard advertisement. Most of the existing literature focused on the influential slot selection problem without considering any specific zonal influence constraint. To bridge this gap in this paper, we introduce and study the Influential Billboard Slot Selection Problem Under Zonal Influence Constraint. We propose a simple greedy approach to solve this problem. Though this method is easy to understand and simple to implement due to the excessive number of marginal gain computations, this method is not scalable. We design a branch and bound framework with two bound estimation techniques that divide the problem into different zones and integrate the zone-specific solutions to obtain a solution for the whole. We implement both the solution methodologies with real-world billboard and trajectory datasets and several experiments have been reported. We compare the performance of the proposed solution approaches with several baseline methods. The results show that the proposed approaches lead to more effective solutions with reasonable computational overhead than the baseline methods.