We study the behaviour of edge states in Rice-Mele model with Hubbard interaction, $U$, at half-filling using density matrix renormalization group, exact diagonalization and effective charge dynamics in Kumar representation. By increasing $U$ for a fixed dimerization, $\delta$, and staggered potential, $V$, we find the quasiparticle edge states in the charge gap to come down in energy from $V$ in the absence of Hubbard interaction to zero energy at a critical interaction, $U_c\approx 2V$. This presents an uncommon situation where the competition between $U$ and $V$ leads to zero-energy edge states, although individually neither $U$ nor $V$ favours the edge states at zero energy. Upon increasing $U$ further, the edge state energy starts increasing again until they are lost in the bulk. However, upon increasing $U$ even further, these edge states reappear in the high energy gap. So, with Hubbard interaction, the edge states in Rice-Mele chain transmigrate from the low to high energy charge gap.