The Patrolling Problem is a crucial feature of the surveillance task in defense and other establishments. Most of the works in the literature concentrate on reducing the Idleness value at each location in the environment. However, there are often a few prioritized locations that cannot be left unvisited beyond a certain Time Period. In this paper, we study the problem of Prioritized patrolling - the task of patrolling the given environment using multiple agents while ensuring the prioritized locations are visited within the pre-specified Time Period. We present a novel algorithm, namely, Time Period Based Patrolling (TPBP) algorithm, to solve the prioritized patrolling problem. It determines a sequence of walks for each agent online that complies with the Time Period requirement of the Priority nodes while reducing the Idleness of all the other nodes. We have tested and validated the algorithm using SUMO - a realistic simulator developed for traffic management. Since the existing strategies are not designed for Prioritized Patrolling, we show through comparison that proposed algorithm is required to solve the problem.