My kitty does the same thing. He gently paws as the covers. If I ignore him he gets a little more insistent that he come under the covers, pawing harder, even pushing his little face under the edges until he finds an opening. In my case he gets hot or irritated if I shift and leaves, only to repeat the process in an hour. As sweet as it is at first, the third time being woken up, it stops being sweet tho even then I can't refuse him. The tickle of little whiskers on my face and the sound of his purrrrrr in the quiet darkness just melt away any annoyance or anger.
Koal (my midnight snuggler)
Shannon