We investigate the boundary effect of small-scale s quark matter and the self-similarity structure influence of strange hadrons in the hadron gas on quark-gluon plasma (QGP)-hadron phase transition. In this study, the multiple reflection expansion method is used to investigate the boundary effect of QGP droplets containing s quarks. The calculation reveals that under the influence of boundary effect, small-scale s quark matter exhibits that energy density, entropy density, and pressure are all lower. In the hadron phase, there exists a two-body self-similarity structure between K mesons and neighboring π mesons, subjected to collective flow, quantum correlations, and strong interactions. By using two-body fractal model to study the self-similarity structure of the K meson in meson and quark aspects, it is found that the self-similarity structure of the K meson exists in hadron phase, resluting in an increase in the energy density, entropy density, and pressure of the K meson. Furthermore, under the influence of self-similarity structure, the derived transverse momentum spectrum of K meson shows excellent agreement with experimental data (Fig. (a)). This study predicts that in the HIAF energy region, the self-similarity structure factor of K meson q_1 approaches 1.042. Additionaly, under the combined influence of boundary effects and self-similarity structure of K and π mesons, the phase transition temperature of s quark matter increases (Fig. (b)). Morover, if the boundary of s quark matter is more curved, the increase of phase transition temperature becomes more pronounced compared to the effect of self-similarity structure alone.