<p>Lately, an adaptive exponential functional link network and its variants have been employed for nonlinear system identification. The nonlinear filters constructed upon spline exhibit efficacious nonlinear modelling along with lesser computations. However, non-Gaussian interference deteriorates the modelling ability of such nonlinear filters. Therefore, instead of this, the present manuscript intends to present a new exponential inverse square root recursive spline adaptive filter (EISSAF) for nonlinear system modelling. It incorporates a newly proposed exponential inverse square root cost criteria for imparting robustness to the proposed algorithm in the wake of non-Gaussian or impulsive noise contamination. The weight adaptation rule has been derived for the proposed method. Varied numerical simulations assert the potency of the introduced spline-dependent methodology in nonlinear system identification.</p>