  In this work, we investigate the local density of states (LDOS) near a
magnetic impurity in single-layer FeSe superconductors. The two-orbital model
with spin-orbit coupling proposed in Ref. [{\emph{Phys. Rev. Lett.}
\textbf{119}, 267001 (2017)}] is used to describe the FeSe superconductor. In
the strong coupling regime, two impurity resonance peaks appear with opposite
resonance energies in the LDOS spectral function. For a strong spin-orbit
coupling, the superconducting gap in this model is $d$-wave symmetric with
nodes, the spatial distributions of the LDOS at the two resonance energies are
fourfold symmetric, which reveals typical characteristic of $d$-wave pairing.
When the spin-orbit coupling is not strong enough to close the superconducting
gap, we find that the spatial distribution of the LDOS at one of the resonance
energies manifests $s$-wave symmetry, while the pairing potential preserves
$d$-wave symmetry. This result is consistent with previous experimental
investigations.
