With the rising number of patients along with the same time, the comparative evolution in wireless technology has made Body Sensor Networks (BSNs) flourishing in the market. In BSNs, tiny biosensor nodes are deployed inside/outside of a human body to continuously monitor patient vital signs such as heartbeat rate, blood pressure, respiratory rate, and temperature. BSNs face various challenges due to their constrained natured environment. These are prioritized, delay less and secure transmission of patient data using a public network, simultaneous reception of patient data by end-users, patient identity privacy, high overhead, and energy constraints. However, various researchers have worked in this domain, unable to cope with all these issues in one go. In this paper, we have proposed a novel cryptosystem covering the mentioned issues in a desirable way. For this purpose, we design a novel concept of a lightweight and secure attribute-based multi-receiver generalized signcryption scheme that can adaptively work as an encryption mode, a signature mode, or a signcryption mode with a single algorithm and consume fewer resources by using shorter keys size of Hyper-elliptic Curve Cryptography (HECC). Similarly, we design a modified priority-based scheduling algorithm to delay less emergency patient data. Multiple end-users access the encoded data simultaneously by defining an access policy using AND & OR logic gates. Furthermore, we simulate our scheme using the AVISPA tool and demonstrate that our proposed scheme can meet the security requirements such as data confidentiality (IND-CCA), integrity, unforgeability (EUF-CMA), patient data authenticity, forward secrecy, and non-repudiation distinctly in the Random Oracle Model (ROM). Due to lower processing costs and transmission overhead, this scheme is more efficient and suitable for the resource-constrained environment of BSNs.