(Aside from, obviously, everything he's ever said about anything.)
His Facade of being "Barack Obama" (implying a sort of exotic mystique of African culture) when he knows full well that Barack Sr. is not his father. His continuously offering up less than fully forth coming birth documents in order to keep the truth about him obscured.
I believe he fears ridicule and worse, loss of votes as a result of people finding out who his real father is, and how he intentionally deceived everyone about it.
An interesting theory, but impossible to prove. As the old saying goes, fatherhood is opinion, motherhood is fact. Everyone thinks they 'know full well' who their father is, but this is territory most Americans aren't going to be interested in traversing. Especially some mothers. ;-)
Given the proclivities of your average politician, you won't find much zeal in pushing the idea of mandatory DNA testing with them, either.
Sorry, but if that's all you've got, then Barryock Hussainvis Soterobama has nothing to worry about. Americans that voted for him like the mystique, and sticking to his story now, when no evidence exists to contradict it, could not be easier.
I think he suspects. I don't think he knows.