<p>This work investigates the theoretical properties and stability mechanisms of semi-infinite gap solitons in moiré optical lattices governed by quartic dispersion. Using the framework of Floquet-Bloch theory, we explore linear modes in commensurate and incommensurate lattice configurations, revealing distinct localization characteristics influenced by the lattice twist angle and dispersion coefficient. Numerical simulations confirm that gap solitons can emerge in a self-focusing Kerr medium, originating from nonlinear evolution of localized linear Bloch modes. Linear stability analysis indicates that solitons are stable under normal quartic dispersion but unstable under anomalous dispersion, corroborated by direct perturbation evolution methods. Additionally, the study highlights the influence of lattice twist strength and angle on soliton localization, with incommensurate lattices enabling thresholdless soliton excitation. These findings provide new insights into the dynamics of solitons in moiré systems, with implications for designing tunable photonic structures and advancing applications in optical communications and nonlinear photonics.</p>