Silveri was arrested at his suburban Philadelphia home late Wednesday after police traced the America Online account to him.
The sexually explicit communications took place over several months on a state-issued laptop found in his vehicle, they charged.
Silveri admitted that he owned and used the AOL screen name, District Attorney G. Michael Green said.
He was being held on $250,000 bail at the Delaware County Prison on charges that include solicitation of child rape. It was not clear if he had a lawyer, and a phone message left at his home was not immediately returned.
The trooper discussed having sex with both the fictitious mother and her girls, and planned a meeting but failed to show, according to a police affidavit.
Silveri, an eight-year veteran of the force, worked in a collision reconstruction unit in Philadelphia. He has been suspended without pay, state police spokeswoman Linette Quinn said.
A preliminary hearing is set for July 30.
