According to Ms. James’s suit, internal documents at Gemini show that just months after Earn was started in 2021, the company’s risk analysis teams deemed Genesis very risky — highly leveraged with limited liquidity. Gemini also knew that Genesis loans were at one point tied up in Alameda Research, the now-bankrupt crypto hedge fund also founded by Mr. Bankman-Fried, who is now being tried on criminal fraud charges.

But Gemini did not share the information with investors, leaving at least 29,000 New Yorkers and hundreds of thousands of others across the country in the dark about the dangers to their assets, Ms. James said.

The lawsuit accuses Genesis and Digital Currency Group of trying to conceal Genesis’ losses from Gemini, Earn investors and the public. The two firms hid the financial troubles last year when Genesis entered into a $1.1 billion, 10-year promissory note with Digital Currency, a deal intended to give the false impression that Genesis was on stronger footing and to encourage investors to keep participating in the Earn program, according to the lawsuit.

“This fraud is yet another example of bad actors causing harm throughout the under-regulated cryptocurrency industry,” Ms. James said in a statement. “My office will continue our efforts to stop deceptive cryptocurrency companies, and to push for stronger regulations to protect all investors.”

Soichiro Moro, the former Genesis chief executive, and Digital Currency’s chief executive, Barry Silbert, were also named in the suit.