Recently, security and privacy issues in mobile communication systems became an enormous challenge due to the limited resources of mobile networks regarding communication overhead, computational cost, and battery power. 5G systems provide high performance and flexibility that can connect billion of objects through Heterogeneous Wireless Networks (HWN) concerning the Internet of Things (IoT). However, some of these security challenges can be addressed by using outsourced assistants such as Server-Aided Verification (SAV) to contribute partially with the authentication process among 5G network entities. In this paper, we propose an efficient and secure identity-based signature scheme with Server-Aided Verification for 5G mobile systems (IBS-SAV). We provide a performance evaluation based on security proof of the proposed IBS-SAV scheme under existential unforgeable in the random oracle model as well as the security against collusion and adaptive chosen message attack (EUF-CMA). The performance evaluation and security analysis demonstrate that our IBS-SAV scheme is not only secure but also can reduce the communication and computation complexity for mobile systems efficiently. INDEX TERMS Public key cryptography (PKC), identity-based signature (IBS), server-aided verification (SAV), 5G mobile systems.