A cryptocurrency exchange that claims real dollars back its popular digital coin Tether raided those reserves to cover up $850 million that went missing, the New York Attorney General’s office said Thursday.

State Attorney General Letitia James said Hong Kong-based iFinex Inc., which operates the Bitfinex cryptocurrency exchange and owns Tether Ltd., has been commingling client and corporate funds to cover up the missing funds, which occurred in mid-2018 and hadn’t been disclosed publicly.

The...