<p>The Talbot effect has been extensively investigated in one-dimensional and orthogonal two-dimensional periodic structures; however, its manifestation in skew-periodic lattices remains unexplored. Here, we investigate the Talbot effect in skew-periodic structures using Laguerre-Gaussian beams with both zero and non-zero radial indices. The skew-periodic structures are fabricated by superimposing two one-dimensional binary gratings with small filling factors, forming rhombus-shaped unit cells with tunable vertex angles. We show that the vertex angle serves as a control parameter for modulating near-field diffraction. At specific angles, self-replication of the incident beam occurs at certain Talbot distances, while slight deviations lead to the Hermite-Gaussian mode arrays. A theoretical model predicts the critical vertex angles for self-imaging and mode transformation, supported by experimental results. We also introduce the vertex-angle Talbot carpet, a tool for identifying true self-imaging planes in skewed lattices by mapping diffraction intensity versus vertex-angle, rather than propagation distance. This approach opens a regime in Talbot physics and enables the generation of structured light fields with adjustable geometries, offering potential applications in optical trapping, lattice-based systems, and multi-atom interactions-providing a low-cost alternative to spatial light modulators.</p><p></p>