First, Xin Qiji has never served as the right prime minister in history; Second, because of his father's contribution, his son's shady official position can't be as big as the right prime minister.
Judging from the quotations, it should be Xin Qing Ji.
"Biography of Han Xin Qing Dynasty" records:
Xin Qingji, with clear pronunciation and mellow voice, rarely regards his father as decent. He followed Hou Changhui to Chigu City, Wusun, Tuntian, and fought with Yunhou, but Chen was defeated.
It means:
Xin Qingji, with a true word, worked for Right School Cheng when he was young because of his father (the official in charge of architecture in the Western Han Dynasty was called "the master" with an annual salary of 2,000 stone, and Right School Cheng was one of his five officials with an annual salary of 600 stone). He followed Luo Longhou Chang Hui to open up wasteland in Wusunchi Valley City, fought side by side with Yunhou, and repelled the enemy from the front.