A judge at the High Court in Edinburgh ordered Lukasz Czapla, 41, who killed two-year-old Julius after splitting up with the boy's mother, to serve at least 23 years before applying for parole.
Czapla had denied murdering the toddler in his home in the city’s Muirhouse, in November 2020.
Now, the Daily Record has reported that Czapla has lodged an appeal at the High Court of Criminal Appeal in the Capital, and a hearing will take place later.
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He has no requested to be released on bail and will remain in custody.
At the trial, Czapla pead guilty to culpable homicide, as he claimed diminished responsibility.
However, prosecutors pushed for a murder conviction, and a jury unanimously found him guilty.
Prosecutor Alan Cameron said the evidence before the jury showed Czapla was motivated by anger and jealousy over Ms Szczesniak's relationship with her new partner.
Outside court, Detective Inspector Bob Williamson, of Police Scotland’s Major Investigation Team, said: "Julius was a bright, happy young boy and his loss in such horrendous circumstances has been devastating for his mother and his family.
"Lukasz Czapla is now facing the consequences of his actions.”
Following the verdict, Julius’ mother, Ms Szczesniak, said: "Every day I think about Juliusz. I can't imagine what his little, helpless heart felt that night and I feel his fear and pain every day. He was part of me, part of my heart and soul.
"I wish I could hug him, play with him and watch him grow.
"Every day I ask myself why there is so much evil in this world, why the innocent have to suffer.
"He not only took Juliusz’s life but my life too.
"That day, the world stopped, not only for me but also for my mother and my sister.
“Despite the breakup with Juliusz's dad, I wanted him to have contact with our son. I never stopped him seeing Juliusz. He loved him like every child loves their dad. He trusted him, he trusted him completely.
"Juliusz was murdered only for revenge. His dad wanted me to suffer, he succeeded and achieved his goal, at the cost of my beloved little boy’s life.”