Blind image quality assessment (BIQA) methods often incorporate auxiliary tasks to improve performance. However, existing approaches face limitations due to insufficient integration and a lack of flexible uncertainty estimation, leading to suboptimal performance. To address these challenges, we propose a multitasks-based Deep Evidential Fusion Network (DEFNet) for BIQA, which performs multitask optimization with the assistance of scene and distortion type classification tasks. To achieve a more robust and reliable representation, we design a novel trustworthy information fusion strategy. It first combines diverse features and patterns across sub-regions to enhance information richness, and then performs local-global information fusion by balancing fine-grained details with coarse-grained context. Moreover, DEFNet exploits advanced uncertainty estimation technique inspired by evidential learning with the help of normal-inverse gamma distribution mixture. Extensive experiments on both synthetic and authentic distortion datasets demonstrate the effectiveness and robustness of the proposed framework. Additional evaluation and analysis are carried out to highlight its strong generalization capability and adaptability to previously unseen scenarios.