Former New York state Assembly Speaker Sheldon Silver used his official position to help two women with whom he was having secret extramarital affairs, prosecutors alleged in materials unsealed Friday in the former lawmaker’s federal corruption case.

In a sealed court filing before Mr. Silver’s corruption trial last fall, the U.S. attorney’s office in Manhattan presented evidence that Mr. Silver granted special access to one of the women, a lobbyist with business before his office, and helped the other woman secure a state...