In addressing the challenge of degraded tracking performance, particularly when dealing with spawning extended targets and the extraction of target trajectories in complex environments, this paper introduces a novel filtering algorithm: Spawning extended target Cardinality Balanced Multi-Target Multi-Bernoulli algorithm based on Trajectory Random Finite Set (S-TCBMeMBer). To enhance the representation of trajectory sequences for multiple extended targets and ensure continuous trajectory information, a Trajectory Multi-Bernoulli Random Finite Set (Trajectory MBer-RFS) is first employed. Following this, a multi-Bernoulli spawning model is developed. This model establishes the equations of motion and dynamic transition models for different spawning extended targets by leveraging trigonometric equations linking the orientation angle of the original extended target and the deflection angle of the spawning extended target. This innovative approach enables joint estimation of the kinematic state and shape state of the spawning extended target. With the integration of the Trajectory MBer-RFS and the newly developed multi-Bernoulli spawning model, the S-TCBMeMBer filter is derived and presented. Additionally, implementations under linear Gaussian conditions, specifically the Gamma Gaussian Inverse Wishart (GGIW) mixture, are provided. Simulation results underscore the effectiveness of the proposed algorithm in tracking spawning extended targets and extracting comprehensive trajectory information even in the presence of clutter, missed detection, and noise.