By most standards, Austin Jia holds an enviable position. A rising sophomore at Duke, Mr. Jia attends one of the top universities in the country, setting him up for success. With his high G.P.A., nearly perfect SAT score and activities — debate team, tennis captain and state orchestra — Mr. Jia believes he should have had a fair shot at Harvard, Princeton, Columbia and the University of Pennsylvania. However, those Ivy League colleges rejected him after he applied in the fall of 2015. It was particularly disturbing, Mr. Jia said, when classmates with lower scores than his — but who were not Asian-American, like him — were admitted to those Ivy League institutions. “My gut reaction was that I was super disillusioned by how the whole system was set up,” Mr. Jia, said. Students like Mr. Jia are now the subject of a lawsuit accusing Harvard of discriminating against Asian-Americans in admissions by imposing a penalty for their high achievement and giving preferences to other racial minorities.