Buddhism was, of course, founded in India. It then spread across Asia and was very influential in many different countries of East Asia. As Buddhism spread, it was influenced by the countries into which it entered. One of these countries (the largest of them) was China. Buddhism entered China with merchants travelling on the silk roads. It may have entered China as early as the second century BCE.
The major effect that China had on Buddhism was to create what Bentley and Ziegler call (on p. 235 of the brief second edition of Traditions & Encounters)”a syncretic faith, a Buddhism with Chinese characteristics.” (This is a play on Deng Xiaoping’s later saying that China should build “socialism with Chinese characteristics.) Bentley and Ziegler point out that Chan Buddhism (called Zen in Japan) was very popular in China. This was in part because many Chinese had been Daoists with little interest in written texts and Chan Buddhism did not emphasize written texts. Instead, it emphasized “sudden flashes of insight.” The Buddhists tailored many of their teachings to seem more familiar to Chinese who had grown up in the Daoist tradition.
In these ways, China affected Buddhism by causing it to adapt and become more familiar and congenial to Chinese culture.