The incident, which took place on Royston Road, happened at about 9pm last Friday.
Dean Jones, 45, and 16-year-old son Lewis Daines - who were cycling along the road - were pronounced dead at the scene.
The car involved, believed to be a red Volkswagen Golf, failed to stop at the scene and was later found abandoned on Bleak Avenue, Shafton.
Police are looking for Paul Yates, 35 - also known Bane or Pip - is being sought in relation to the crash.
A 37-year-old man - who was initially arrested on suspicion of causing death by dangerous driving - has since been released with no further action being taken against him.
A police spokesperson said: “We are appealing for anyone who witnessed the incident or who was driving in the area at the time and may have seen the Golf or cyclists to get in touch.
‘We are particularly keen to hear from those with dash-cam footage.
“Emergency services attended, but sadly both Mr Jones and Mr Daines were pronounced dead at the scene.
“Their family is being supported by our specially trained officers and have asked that their privacy is respected at this difficult time.
“A 37-year-old man was arrested on suspicion of causing death by dangerous driving - he has since been released with no further action after being eliminated from our enquiries.”
Police believe the car was travelling towards Cudworth when it struck the pair and detectives are attempting to trace its driver.
‘You can pass information to police via our new online live chat, our online portal or by calling 101,” the spokesperson added.
“Were you travelling along Royston Road that evening?
“Did you see the vehicle prior to or after the collision?
‘Please quote incident number 1089 of January 20 when you get in touch.
“Alternatively, if you prefer not to give your personal details, you can stay anonymous and pass on what you know by contacting the independent charity Crimestoppers.
“Call their UK contact centre on freephone 0800 555 111 or complete a simple and secure anonymous online form at crimestoppers-uk.org.”