Beam hopping (BH) has great potential to improve satellite resource utilization and business service capabilities through time slicing. During the BH pattern design, most existing studies focus on the communication requests satisfaction, which ensures high throughput communication for each user. Since all users have a priority order during service, the service fairness among users is hardly guaranteed, which has rarely been considered. Therefore, in this paper, we investigate a joint latency tradeoff and service satisfaction design in the BH satellite system. To be specific, we propose a beam-cluster scheme to design the BH pattern to avoid co-channel interference under spectrum sharing, where all beams are uniformly clustered for service fairness at the cluster level. Besides, a multi-objective optimization problem for minimizing the latency and maximizing the capacity-request ratio is proposed to ensure service fairness at the beam level. To simplify the multi-objective optimization problem, the allocated time-slot number to beams is determined according to requests. Moreover, the value function is adopted, and the Delay-Fairness-Service-Value-Optimal (DFSVO) algorithm is proposed to obtain the BH pattern. Lastly, the simulation results demonstrate the superiority of BH technology and the proposed DFSVO algorithm when compared with the traditional fixed allocation scheme, which ensure low latency and a high capacity-request ratio 1 .