In the Attack on Titan wikia they say that the Ackerman clan can "manifest "the power of the Titans" as humans, without becoming a Titan". What does this mean exactly? The titans have regeneration and a huge strenght which I doubt the Ackerman clan have, even if they are above average humans. So, what would those powers be then?
In AoT: It was said that the attack titan is able to see the memories of the past and future users. It is also said that the Ackerman's are able to draw upon the collective knowledge of past Ackermans. One of the main reasons he's so good against the titans, the same with Mikasa. But since she's younger she hasn't had as much time to see their memories as Levi has. (Will update with sources when I find them) In the meantime, I hope this helped.
As far as I know, the king of the walls made some changes in their gene. first, they protect the king with their life. to do so, in some acute situation they can become as powerful as a titan (physical power I mean :D)
it's called the
Awakened power for more information about it you can check this out