Does Edmund kiss Reepicheep in the voyage of dawn treader?

No, Edmund does not kiss Reepicheep in *The Voyage of the Dawn Treader*. There's no romantic or even particularly close interaction between the two characters in the book.

Reepicheep is a talking mouse, and while he's a brave and noble character, the book doesn't depict any sort of romantic relationship between him and any of the humans.

Perhaps you're thinking of a fan interpretation or a different piece of media inspired by the book.