The 30-year-old's father Max Sica was jailed for a minimum of 35 years for the 2003 murders of former girlfriend Neelma Singh and her siblings Kunal and Sidhi.
Daniel Sica pleaded guilty on Monday - the day after his birthday - to trafficking, with the Brisbane Supreme Court being told his criminal history includes trying to flee the dock during an appearance on other charges.
Sica admitted being a frequent street level meth dealer, while occasionally supplying wholesale amounts.
He made 30 sales to 29 customers over about three months.
Police found a counterfeit note, two phones containing messages revealing his trafficking business, and meth and cocaine when they searched his apartment on May 2 last year.
He was on probation at the time.
The father-of-two was drug dependent, consuming large quantities of meth, and associating with other users and dealers at the time he offended, defence barrister James Godbolt said.
"Drugs were his undoing as they have been in the past," Mr Godbolt told the court.
His motivation was "unquestionably commercial" but directed at feeding his own drug habit, he added.
The court heard he had a a lengthy criminal history, starting from the age of 21, that included charging at a police prosecutor before biting him on the arm after he tried to flee the dock.
A corrective services officer was also injury during the escape attempt.
Prosecutor Elise Sargent said the trafficking had occurred over a short period, but was intensive and showed an escalation in Sica's drug offending.
Justice Paul Freeburn said he noted Sica's "difficult family history" mentioned when another judge handed down a previous sentence.
Sentencing him to five-and-a-half years' jail, Justice Freeburn ordered Sica be eligible to apply for parole immediately.
Sica has been in custody for about 19 months since his arrest last year.
The court heard the Parole Board has experienced delays of up to eight months in processing applications.
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