  Due to the topological nature of Aubry-Andr\'{e}-Harper (AAH) model, exotic
edge states have been found existing in one-dimensional periodic and
quasiperiodic lattices. In this article, we investigate continuous-time quantum
walks of identical particles initially located on either edge of commensurate
AAH lattices in detail. It is shown that the quantum walker is delocalized
among the whole lattice until the strength of periodic modulation is strong
enough. The inverse participation ratios (IPRs) for all of the eigenstates are
calculated. It is found that the localization properties of the quantum walker
is mainly determined by the IPRs of the topologically protected edge states.
More interestingly, the edge states are shown to have an exotic
`\emph{repulsion}' effect on quantum walkers initiated from the lattice sites
inside the bulk. Furthermore, we examine the role of nearest-neighbour
interaction on the quantum walks of two identical fermions. Clear enhancement
of the `\emph{repulsion}' effect by strong interaction has been shown.
