Sam Imrie was found guilty of “glorifying” terrorists online and collecting information which could be useful to committing acts of terror.
The 24-year-old was convicted after trial at the High Court in Edinburgh in October and sentenced to seven-and-a-half years earlier this month.
Now Imrie’s legal team has lodged an intention to appeal against his conviction and the length of his imprisonment.
Imrie had denied the offences but guilty verdicts were returned by a jury on eight of the nine charges against him.
He was cleared of preparing to commit acts of terrorism, which included suggesting online that he planned to live stream an attack on the Fife Islamic Centre in Glenrothes.
Imrie called Norwegian terrorist Anders Breivik – who killed 77 people in 2011 – “the saviour of Europe” and claimed to have written to him in jail.
He referred to Brenton Tarrant – the monster who carried out the 2019 Christchurch mosques mass shootings which left 51 dead – as “Saint Tarrant”.
And he possessed “manifestos” written by Breivik and Tarrant which prosecutors said could help advice someone bent on their own terror attack.
An appeal court spokesman confirmed the intention to appeal had been lodged.
He added Imrie’s lawyers now had until February 8 to set out submissions on the grounds of appeal he will argue in court.
Imrie was convicted of “glorifying” terrorist acts committed by Breivik, Tarrant and others between June 22 2018 and July 4 2019 on Facebook and Telegram.
He was found guilty of collecting information likely to be useful to a person committing or preparing an act of terrorism between June 20 and July 4 2019.
But jurors found him not guilty by majority of preparing to commit acts of terrorism by building up an “arsenal” of weapons, indicating online that he planned to stream live footage of “an incident”, going to the Fife Islamic Centre with a petrol can, and trying to access the building.
Imrie was convicted of wilfully setting fire to the doorway of a derelict building at Strathore Lodge, Thornton, and setting ablaze foliage around a headstone at St Drostans Cemetery, Markinch, both on July 4 2019.
He was also found guilty of possessing “extreme pornographic images” depicting sexual activity involving a human corpse and possessing child pornography.
Sentencing Imrie, judge Lord Mulholland told him: “You posted on a neo-Nazi chatroom your hatred of Muslim, Jews, black people and refugees.
“You revered neo-Nazi and white supremacists. You lauded their crimes against innocent people.
“You were spreading hate and encouraging others to take terrorist action that you pretended you had.
“Your conduct was despicable.”