Cloud computing is the provision of on-demand computing resources over the internet and on a pay-as-you-go basis, ranging from software to computation power. Task scheduling and its execution is a fundamental requirement of cloud environment. However, dynamic scheduling of tasks on basis of priority is a challenging area such that the tasks finish before their deadline. Earliest Deadline First (EDF) has been considered in literature for task scheduling to meet the deadlines. However, basic EDF (i.e., which schedules tasks on basis of deadline only)is not suitable for cloud environment. Therefore, this work proposes modified Preemptive EDF (p-EDF) and Non-Preemptive EDF (np-EDF) algorithms considering task priority and cloud provider cost. As both algorithms have their own merits and de-merits, a hybrid EDF is further proposed which makes decision dynamically whether to cause preemption or not, using a Determiner function. The objective of the work is to avoid unnecessary wastage of CPU power and time due to unnecessary preemptions, along with avoiding unnecessary deadline misses such that the high priority task does not wait for the low priority task to end. Simulation results show that the proposed algorithm outperforms other considered benchmark scheme for different performance parameters such as Deadline Miss Count, Preemption Count and average waiting time.