SBAS is mainly used in civil aviation and navigation, and will be applied to autonomous driving in the future. Given the open signal format of the Satellite Based Augmentation System (SBAS), which exposes security threats such as spoofing attacks, the utilization of SBAS navigation message authentication technology can improve the SBAS anti-spoofing ability from the system side. SBAS message authentication technology has become the future direction of SBAS system development. However, during the initial design of SBAS on L1, message authentication technology was not considered, and the addition of authentication messages will lead to further strain on existing message bandwidth resources. Therefore, in response to the issue of insufficient bandwidth resources after adding authentication messages to SBAS L1, a study on message scheduler for SBAS L1 authentication was conducted. A fixed time sequence dynamic message scheduler for incorporating authentication messages was proposed. This scheduler reduces the frequency of broadcasting clock error parameters to mitigate the impact of adding authentication messages. Furthermore, an optimized fixed time sequence dynamic message scheduler based on SBAS clock error messages was introduced. The results show that the message scheduler can not only improve the flexibility of SBAS message broadcasting, but also shorten the update interval of various types of messages under the premise of meeting the maximum update interval requirement. With minimal impact on the maximum message update interval, it improves the integrity, authenticity, and availability of messages. This approach can increase the effective message ratio in SBAS to over 91%, and the optimal solution reduces the initial user positioning time to 26 s.