Parametric sampling of complex exponentials is a problem widely studied in harmonic analysis and it has wide applications in radar, communications, near-far and other fields. One of the approaches to estimating complex exponentials is Prony's method which allows estimation of K exponentials from 2K samples. In practice during digital acquisition using Shannon's framework, the amplitude is bounded by the dynamic range of the ADC. This is overcome by the Unlimited Sensing Framework. In this paper, we propose an approach that mimics Prony's method and can estimate the parameters of complex exponentials without any sampling rate requirements from 6K samples. This strategy uses multi-channel USF architecture that can implement either real-valued or complex-valued thresholds based on Gaussian integers. Lastly, we present the effect of quantization noise on the performance of both estimation strategies, and calculate the Effective Number of Bits and show that four quantization bits are sufficient for sub-Nyquist frequency estimation.