Officer Denning first appeared in Rocksteady Game's Batman: Arkham City in October 2011.
Denning is an officer in the Gotham City Police Department and a member of the volunteer strike team operation undercover in Arkham City.
Arkham City Incident
Denning volunteered to join the strike team operating undercover in Arkham City. He and nine other members of the team infiltrated Penguin's gang. Unfortunately, the team's cover was blown by Hugo Strange during one of his interviews with Penguin and they were taken hostage, where they were subjected to random beatings and torture inside the Museum, specifically the Iceberg Lounge.
Denning, along with Officer Southwold, are taken to the Iceberg Lounge when Batman infiltrates the Museum. Once outside the lounge, The Penguin comes on the intercom and forces Batman to listen as he freezes Denning's hand and shatters it with a hammer.
After Batman disables The Penguin's gun and kicks him off the ice tower, The Penguin detonates multiple explosive charges placed around the tower. However, the explosion does not kill him.
He is later identified as the injured officer on the ground by the exit of the museum. If you speak to Officer Jones multiple times he will state that Denning was injured when the ninja escaped. He has both hands at this time as well.
Denning is the cop messing with Penguin's umbrella when the undercover cops take refuge in the Iceberg Lounge after Two-Face takes control of the rest of the museum.
After Arkham City Incident
When the GCPD stormed the mega prison the undercover cops were rescued Denning included.
Arkham Knight Incident
Denning seems to have been promoted some time between the events of Arkham City and Arkham Knight because he is seen in the holding cells talking about Officer Owens with another officer. It says in the subtitles Sergeant Denning.