The Supreme Court sacked Sharif in late July following an investigation into corruption allegations against him and his family, making him the 15th premier in Pakistan's 70-year history to be sacked before completing a full term.
In a lengthy petition demanding that his case be reviewed, Sharif's legal team laid out 19 points challenging the court's judgment, saying the ruling suffered "from errors floating on the surface".
"The petitioner seeks review of the final order of the court," read the application filed late Tuesday, according to a copy seen by AFP.
The Supreme Court has also ordered the country's anti-corruption watchdog, the National Accountability Bureau, to open a criminal case against Sharif, his sons - Hussain and Hassan - and his daughter Maryam.
Jan Achakzai, a PML-N official, told Reuters Sharif had filed three separate appeals in the Supreme Court.
"It is our right to seek a review," he said. "People of Pakistan haven't accepted the decision."
Achakzai said the same five-judge panel that decided on the disqualification would likely hear the review petitions.
Sharif's disqualification stems from the Panama Papers leaks in 2016 which appeared to show that Sharif's daughter and two sons owned offshore holding companies registered in the British Virgin Islands and used them to buy properties in London.
In April, the Supreme Court ruled that there was insufficient evidence to remove Sharif from office - by a split 2-3 verdict - over the Panama revelations but it ordered further investigations into his family's wealth.
The judges in July alleged Sharif did not declare a small source of income that the veteran leader disputes receiving.
Achakzai said the appeals sought a review of the disqualification on the basis that two of the five judges, who had already given a dissenting note in April's verdict, were not supposed to sit on the panel that gave the final ruling.
Sharif has kept a grip on the ruling PML-N party, which has a solid majority in parliament, and elected one of his loyalists, Shahid Khaqan Abbasi, as his replacement within days of the court decision.
Critics say Sharif remains in control of the country through Abbasi and is trying to undermine the judiciary.
Sharif's aides say he shows no signs of leaving politics and he recently called the Supreme Court ruling against him "an insult to the mandate of 200 million voters."
Last week he started a so-called homecoming "caravan" procession across the Punjab region where he derives his voter base, from the capital Islamabad to the eastern city of Lahore, drawing large crowds along the way.