Small degree isogenies between conjugate principally polarized superspecial abelian surfaces

Let $p>3$ be a prime number. We prove that every principally polarized superspecial abelian surface over $\mathbb{F}_{p^{2}}$ with $p^{2}$-Frobenius $[-p]$ admits a separable polarized isogeny to its Frobenius conjugate with multiplier at most $(p^{3}/2)^{1/5}$. This generalizes a recent result of A