Which sub-field of psychology deals with differences in human intelligence? As in, what makes someone an intellectual genius?
Broadly speaking, the study of individual differences in psychology is called differential psychology. Psychometrics is the study of psychological measurements, an extremely important part of intelligence research.
Or, maybe a bit more humbly, why are some people more intelligent than others?
The subfield that has been most important in establishing why some people are more intelligent than others is probably behavioural genetics. This field has been at the forefront of creating experimental designs that can give evidence for the causes of individual differences.
However, these fields overlap. It can sometimes be difficult to difficult to say when something is research in field X or Y (And often not important exactly which field you would categorize it as).
It would help if you could also mention some leading thinkers in this field (or any good resources to read more about these topics)
There are many important researchers who study intelligence and why people differ intellectually. Here are a few examples of books that talk, in part, about why people differ in intelligence.
(1) "Intelligence" by Stuart Ritchie. This is a short introduction to intelligence research and is easy to read.
(2) "The Neuroscience of Intelligence" by Richard Haier. This book is slightly longer, but is still fairly easy to read. This book focuses on the actual brain itself.
(3) "The g Factor" by Arthur Jensen. This is a more detailed and complex book. It's not as new as the others but is considered a classic.
However, if you're talking specifically about high intelligence then there are only a few leading researchers.
There have been several leading figures if you go far enough back. All the way from Francis Galton to Lewis Terman to Julian Stanley. Two of the most important current researchers are David Lubinski and Camilla Benbow. They are leading the Study of Mathematically Precocious Youth (SMPY), which is a longitudinal study of highly intelligent individuals. See the link for several publications from the study.
If I could give only a single article (on the subject of very high intelligence) for you to read, it would be the following:
Lubinski, D. (2016). From Terman to today: A century of findings on intellectual precocity.
This is a review of the findings of the study of highly intelligent individuals.
There are other researchers that are important, of course. One other I know who researches high intelligence and high achievement is Jonathan Wai, see his blog if you interested. I'm sure other people could refer to several other important researchers.