Our AI in question inhabits a synthetic brain housed in an organic and genetically modified human body (With a few other cybernetics). This body/brain combination was the result of a black project aimed to create super-soldiers (Why is it always super-soldiers?), and every synthetic brain produced as part of that project was populated with an actual brain. Synthetic brains are also used to treat certain brain disorders, but are incredibly expensive and with medical technology, generally not needed. The ones used by the black project are of a different make, of course, but largely indistinguishable. You can't have a secret operation if one scan your subject reveals they're really not human.
Now, we have an AI that inhabits one of these bodies. They are, however, given false memories, and their emotional/logical/etc programming is on par with what a human would think. Of course, they think better, clearer, faster than a human - But that can be attributed to the black project modifications.
The AI is aware that they were part of this black project, but are led to believe they are like the other "participants" in the project - Enhanced humans, for the most part. A few clones. A few genetically modified clones.
AI in general are rare, but known of. They typically occupy government and military positions, although a handful are useful to large corporations. The power of these AI is, of course, linked to the physical size of their processing unit(s). Think of a modern server farm - Sure, you CAN process stuff on your desktop, but running it in a server farm is much, much better.
Similarly, AI at a smaller scale is capable, but it isn't absurdly better than an actual human. For that you require large constructs. So, a human-sized AI wouldn't be extremely better than a human - Of course, they'd be good at math and logic, but there are people who have been ridiculously good and fast at those.
The AI believes they are "human" - But are given some form of argument that convinces them they might not be what they think they are. How would they go about proving they are (or aren't) an AI?
I realize a lot of what I've said seems to be in the vein of making them impossible to detect - But this is not the intent. It is simply there to restrict the AI to a degree that they could reasonably believe they are human - And so would others. Differences are detectable, with great effort.