We present a simple prototype study of electromagnetic radiation by a one-dimensional quasiperiodic Fibonacci-type array laid on a grounded dielectric slab, extending our previous free-space studies. Analytic parameterization of the interaction between aperiodic-order-induced “quasi-Floquet” waves and slab-induced surface/leaky-waves is addressed, for infinite and truncated arrays, via generalized Poisson summation and uniform asymptotics. Accuracy and computational effectiveness of the proposed parameterizations are assessed via numerical comparisons against an independently-generated reference solution (element-by-element synthesis).