The spline adaptive filtering (SAF) algorithm-based information-theoretic learning has exhibited strong convergence performance in nonlinear system identification (NSI), establishing SAF as a promising framework for adaptive filtering. However, existing SAF-based methods suffer from performance degradation under generalized Gaussian noise (GGN) environment and exhibit significant steady-state misalignment under impulse noise. Moreover, prior research on SAF algorithms has not effectively addressed the adverse effects caused by outliers. To overcome these challenges, the generalized modified Blake-Zisserman robust spline adaptive filtering (SAF-GMBZ) algorithm is proposed. Compared to conventional SAF algorithms, SAF-GMBZ exhibits superior learning performance in GGN. Furthermore, the mean convergence ranges of the step-sizes and the steady-state mean-square error (MSE) are calculated by introducing the commonly utilized assumptions. To arrive at good convergence accuracy and noise cancellation capability in active noise control (ANC) application, the filter-c GMBZ (FcGMBZ) algorithm is further developed based on SAF-GMBZ. Simulation results confirm the accuracy of the theoretical steady-state MSE, and the superiority of the SAF-GMBZ algorithm under GGN environment in NSI, along with the effectiveness of the FcGMBZ algorithm in ANC application under impulsive noise environment.