Mrs Khan said: "Ayesha is only two years old, she cannot even reach the pedals of a car and can only just ride her bicycle."
Ayesha was allegedly flashed by a speed camera in on the A638 near York Road, Doncaster.
Police finally admitted they had made a mistake after Sharna proved she was in Huddersfield as the time and the car's registration didn't match their car.
Mrs Khan said: "At first I assumed someone had been caught for speeding and just give a false name, but the ticket was issued from a speed camera.
"If the car that was speeding on the police system registered to Ayesha, then they would have needed her details to insure and register the car."
Dad Mohamed, 32, said: "Ayesha has not even left the house on her own yet. If there is an ID fraud going on I want the police to help us get to the bottom of it.
"I do not want anything on any records that may harm her future ? that must not happen."