<p>We investigate the phenomenon of normal and higher-order photon antibunching within the framework of the Jaynes-Cummings model which describes the interaction between a single-mode field and a two-level atom by considering different states of the atom such as ground and excited state. Normal photon antibunching in this model has been widely studied using the second-order correlation function (Dung in Commun. 90:322, 1992;Ren et al. in Opt. Express 30:21787, 2022;) but detailed investigations of higher-order photon antibunching based on factorial-moment approaches are still limited in the literature. In the present study, normal as well as higher-order photon antibunching are analyzed using the criterion introduced by Lee (Phys. Rev. A 41 1721 (1990).) which allows a more comprehensive assessment of nonclassical photon statistics beyond earlier studies on second-order correlation. This study explores the dependence of normal and higher-order photon antibunching on the interaction time for various photon numbers. The results are systematically presented and illustrated through graphical representations, with a comprehensive analysis of the underlying dynamics. The results indicate that higher-order photon antibunching reveals stronger nonclassical behavior and the antibunching effect is more pronounced when the atom is initially in the excited state. This study therefore provides a deeper understanding of nonclassical light generation relevant to quantum communication applications.</p>