Precise point positioning can provide accurate coordinates to users without reference stations, and the high-precision real-time clock offset product is necessary for real-time precise point positioning application. As an integral part of the third generation BeiDou Navigation Satellite System, Precision Point Positioning Service provides dual systems (BDS-3 and GPS) real-time PPP services with centimeter- and decimeter-level accuracy for static and kinematic positioning users around China, respectively. However, there exist inconsistent biases in the clock offset of Precision Point Positioning Service, which will negatively affect the positioning and timing performance of the service. By comparing with the post-processing clock offset, this paper verifies that the broadcast clock offset has smaller and more stable biases in the long term and proposes a regional clock offset estimation strategy using broadcast clock offset for a priori constraint. The results show that the new algorithm can effectively reduce the bias in PPP-B2b clock offset. The new clock offset product could improve convergence speed by 25% and 10% in the horizontal and vertical directions. For positioning accuracy, the improvement is 22% and 17%. The absolute error of timing can also be reduced by 60%.