Any such function or elisp script? I want the equivalent function as vi\" sequence in vim.
Try the key sequence C-M-u C-M-SPC (i.e., while holding the Control and Meta keys, press u and Space in sequence), which executes the commands backward-up-sexp and mark-sexp.
I made a mistake: backward-up-sexp doesn't exist in standard Emacs. I wrote it exactly because of the problem mentioned in lkahtz's comment, that the existing function backward-up-list won't work when point is between double quotes.
(defun backward-up-sexp (arg)
(interactive "p")
(let ((ppss (syntax-ppss)))
(cond ((elt ppss 3)
(goto-char (elt ppss 8))
(backward-up-sexp (1- arg)))
((backward-up-list arg)))))
(global-set-key [remap backward-up-list] 'backward-up-sexp)