We investigate the boundary effect of small-scale $ \text{s} $ quark matter, and the self-similarity structure influence of strange hadrons in the hadron gas on QGP–hadron phase transition. In this study, the multiple reflection expansion method is employed to investigate the boundary effect of QGP droplets containing $ \text{s} $ quarks. The calculation reveals that under the influence of boundary effect, small-scale $ \text{s} $ quark matter exhibits lower energy density, entropy density, and pressure. In hadron phase, there is the two-body self-similarity structure between $ \text{K} $ meson and neighboring π mesons under the influence of collective flow, quantum correlations, and strong interactions. By applying Two-Body Fractal Model to study the self-similarity structure of the $ \text{K} $ meson in meson and quark aspect, it is found that the self-similarity structure of the $ \text{K} $ meson exists in hadron phase, leading to an increase in the energy density, entropy density, and pressure of the $ \text{K} $ meson. With the influence of self-similarity structure, it is found that the derived transverse momentum spectrum of $ \text{K} $ meson has a good agreement with experimental data (Fig. (a)). This study predicts that in the HIAF energy region, the self-similarity structure factor of $ \text{K} $ meson $ q_{1} $ approaches $ 1.042 $. Under the influence of boundary effect and self-similarity structure of $ \text{K} $ and π mesons, it shows that the phase transition temperature of $ \text{s} $ quark matter increases (Fig. (b)). And if the boundary of $ \text{s} $ quark matter curves more, the increase of phase transition temperature becomes more pronounced compared to the influence of self-similarity structure.