Who was the first to study the sun?

There was no known first person to study the sun.

There have been many people through history to make notable contributions to our understanding of the sun. Eratosthenes, a greek scholar, was the first known to estimate the distance from the earth to the sun. Aristarchus of Samos was the first to propose that the planets orbited the sun, putting forward the idea of heliocentrism. It wasnt until the 1930's that Subrahmanyan Chandrasekhar and Hans Bethe developed the model of internal fusion and radiation that keeps the sun burning.

Before recorded time, though, people have looked up at the sun, studied it and its movement. For thousands of years before recorded history people have made stone configurations and clocks, cave paintings of the sun.