On the composite thin-film composed of platinum metal and amorphous silicon, periodic structures with oxidation periodicity induced by s-polarized laser, far from the central axis, and tilted outer structures are observed under oblique incidence conditions. First, the generated stripe structures exhibit a leaf vein-like pattern, neither parallel nor perpendicular to the polarization direction of the laser. Second, the structural orientation generated during dynamic scanning is single and dependent on the scanning direction. Finally, the period of the structure decreases with increasing incident angle. These phenomena differ from typical laser ablation periodic structures. This discovery provides more possibilities for regulating laser-induced self-organization.