Child killer Warren Ross, who relentlessly beat a two-year-old girl into unconsciousness and left her sitting in a pram for two days until she stopped breathing, has sought to have his sentence reduced on the basis that he faces "onerous jail conditions".

Ross was found guilty of murdering his girlfriend's daughter, Tanilla Warrick-Deaves, after weeks of abuse and was sentenced to a maximum jail term of 40 years with a non-parole period of 30 years in May 2014.

Warren Ross was sentenced in 2014 to a maximum jail term of 40 years with a non-parole period of 30 years. Credit:Dean Sewell

But defence barrister Chris Bruce, SC, told the NSW Court of Criminal Appeal on Tuesday that his client should have received a discount in his sentence due to the "ongoing fear of violence and intimidation" he would experience in prison as a result of his status as a child killer.

The court heard that Ross had been assaulted in prison, was constantly afraid, and claimed that "someone had a price on his head".