<p>In this research, we delve into the complex dynamics of peakon and pseudo-peakon solutions within the framework of generalized higher-order <i>b</i>-family Novikov equations. The analysis meticulously examines the weak solutions of the <i>J</i>-<i>b</i>F Novikov equations across a broad spectrum of <i>J</i> values, revealing the intricate interplay between nonlinearity and higher-order dispersion that shapes these solutions. As <i>J</i> increases, we observe a transformation in solution structures, evolving into more complex forms characterized by the emergence of higher-order pseudo-peakons with sophisticated derivative discontinuities. Symbolic verification confirms the existence of these solutions, anchoring them in the realm of theoretical reality. Additionally, this research identifies both <i>b</i>-independent and <i>b</i>-dependent peakon solutions, uncovering previously unreported solution structures and their dependence on the parameter <i>b</i>, highlighting their adaptability and resilience under varying dispersive conditions. The explicit role of the parameter <i>b</i> in solution formation and stability underscores the delicate balance necessary for these structures. Through symbolic computation and graphical analysis, we rigorously verify the existence of both <i>b</i>-independent and <i>b</i>-dependent solutions, revealing how higher-order dispersion induces novel discontinuities in derivative orders. Our results establish a unified framework for understanding soliton dynamics in <i>b</i>-family systems, bridging theoretical gaps between low- and high-order integrable models.</p>