There are a few different ways I would answer this question depending on how you actually plan to write this story. I will interpret it in a few different ways and give answers below.
Is there a field of math learn-able by only a few individuals?
Another answer already pointed this out, but the vast majority of human knowledge can be understood by the vast majority of humans (if they put in the effort). The psychological literature is becoming saturated with evidence that learning and performance are more inhibited by self-consciousness than by innate intelligence (which has been shown to be flexible). Here is some research on the topic:
Trait beliefs that make women vulnerable to math disengagement
Conceptions of ability: Nature and impact across content areas
Mind-Sets Matter: A Meta-Analytic Review of Implicit Theories and Self-Regulation
Is there a field of math which very few individuals have taken the time to learn?
Yes, more than I could possibly list. People already named several examples of this in other answers, and if you'd like more examples you could go to the faculty directory of any univeristy math department, and look at what the different mathematicians are interested in.
In your question you specifically mention that you'd like a topic that is introduced in graduate courses in mathematics, not undergraduate courses. Note that topics which are introduced in undergraduate courses are still actively researched; for example, people still do research on things like integration methods.
However, I will try to address that part of your question. In the US, most undergraduate curriculums for math majors require an understanding of basic analysis and algebra, but not so much geometry or topology. In their early graduate years, students will usually be introduced to things like algebraic topology and differential geometry.
If you plan on having a character attend a class on algebraic topology or differential topology, please bear in mind that they must first understand abstract algebra and calculus, respectively. This is important regardless of the topic you choose, as you risk breaking realism for people who know how learning math works.
What is an impressive mathematical feat that would demonstrate how intelligent this drug makes kids?
This interpretation might be a bit off from your original question, but I think it might do you good to consider it. Instead of saying "and then the child could do advanced fractal chaos math" what if instead you specifically named an unsolved problem that the child solved?
You can find a long list of unsolved problems here.
I think you should really consider this approach because it is potentially more engaging for your readers.
On the one hand, you could pick a field of math that has an esoteric-sounding name and then pick an open problem in that field which seems interesting. There isn't anything necessarily wrong with this approach, the only drawback is that readers may run into a brick wall of prerequisites if they try to understand the problem that you select.
Another approach might be to select a problem that anyone can understand: Goldbach's conjecture, the twin prime conjecture, and the Collatz conjecture are all examples of famous open problems that are extremely simple to state. This way, the reader might learn something that they actually have the prerequisite knowledge to understand. This could potentially improve the reader's engagement, but the choice is ultimately up to you.