<p>This paper proposes a novel class of first-order self-exciting hysteretic integer-valued autoregressive (SEHINAR(1)) time series models, in which the stochastic process is conditionally distributed based on past data within a hysteretic autoregressive framework. The basic probabilistic and statistical properties of the proposed model are thoroughly explored. Parameter estimation is obtained via conditional least squares, weighted conditional least squares, and maximum likelihood methods, with the corresponding asymptotic properties rigorously derived. A search algorithm is developed to determine the two boundary parameters, and the strong consistency of the estimators is formally established. Extensive numerical experiments and a real-world data application are provided to demonstrate the practical effectiveness of the proposed method.</p>