Dalek puppet

Dalek puppets were beings who had been taken by the Daleks and partially converted via nanogenes to serve them as slaves. The nanogene automatically would convert any organism it came in contact with, living or dead, making them into a Dalek puppet. These slaves were used as sleeper agents. When activated, they would have a miniature Dalek eyestalk extend from their forehead and a miniature Dalek gunstick from their hand. Later versions didn't have a gunstick emerge from their hand, instead they outstreached their arm and a beam came out of their hand. They could also emit a charge that stopped the victim from moving by making contact with them.

The process occurred when any unprotected non-Dalek entered the Dalek Asylum; the air contained a nanocloud that would slowly convert the victim into an unwitting servant of the Daleks. Not even death could protect them from this fate: the conversion process worked on dead and living flesh alike, and could turn innocent corpses into shambling, zombie-like creatures. Time Lords could not be converted by this means. All intact bodies of the Alaska had this fate befall them, apart from Oswin Oswald, who was entirely converted to a Dalek by the unhinged inmates. (TV: Asylum of the Daleks)

Jenibeth Blakely was captured by the Daleks at a young age and was kept as a prisoner for many years before being turned into a Dalek puppet. However, she was able to resist the control because she still had the mind of a child. She attacked the Dalek Time Controller and destroyed some of its guards, forcing it to retreat. (PROSE: The Dalek Generation)

During the Siege of Trenzalore, the Daleks attacked the Papal Mainframe and converted everyone into Dalek puppets, including the Silents. Tasha Lem, however, was able to resist her conditioning and destroyed three Daleks that threatened the Eleventh Doctor and Clara. (TV: The Time of the Doctor)

At some point, Bors was converted into a Dalek puppet, and located the TARDIS for the Daleks. (TV: The Magician's Apprentice)

More primitive progenitors of the Dalek puppets were the Robomen, who were prisoners on whose brains the Daleks operated in a surgical procedure called the Transfer, fitting them with large, helmet-like headsets. The Daleks' mind control technique was unstable, and the Robomen would eventually go insane and commit suicide. (TV: The Dalek Invasion of Earth) The eyestalk extending from Dalek puppets' foreheads made them visually reminiscent of Dalek Troopers. (TV: Resurrection of the Daleks)

Behind the scenes
Many enemies in the Doctor Who: Legacy mobile game are Dalek puppets of allies or other enemies, including Silent, Tasha Lem and several Church members.