Jerry Yu has the trappings of what the Chinese call second-generation rich. He boasts a Connecticut prep-school education. He lives in a Manhattan condominium bought for $8 million from Jeffrey R. Immelt, the former General Electric chief executive. And he is the majority owner of a Bitcoin mine in Texas, acquired last year for more than $6 million.

Mr. Yu, a 23-year-old student at New York University, has also become — quite unintentionally — a case study in how Chinese nationals can move money from China to the United States without drawing the attention of authorities in either country.