The Dhaka court also handed down life imprisonment to the accused of blasting bombs on the same day in 1989 at the house of Hasina, Dhaka Tribune reported.
The court imposed a fine of 20,000 taka ($240) each on the convicts — members of the Bangladesh Freedom Party (BFP), which was behind the killing of Bangladesh's first president and the Father of the nation Bangabandhu Sheikh Mujibur Rahman in 1975, the report said.
Judge Mohamed Zahidul Kabir of Dhaka Fourth Additional Metropolitan Sessions Judge's Court delivered the verdict, the report said.
One of the accused, Lieutenant Colonel (retired) Abdur Rashid, had previously been sentenced to death for the murder of Bangabandhu, father of Hasina, 70.
The convicts were sentenced to 10 years imprisonment each in two separate charges, a total of 20 years, the report said.
One accused was acquitted as the charges brought against him were not proved.
According to the case, seven or eight armed members of the BFP came to the residence of Bangabandhu in Dhanmondi arwa on August 11, 1989 on two three-wheelers, the report said.
Bangabandhu, the Father of the nation and first president of Bangladesh, was assassinated in 1975. He is considered to be the driving force behind the independence of Bangladesh.
Forcing into the residence, they hurled grenades and opened fire at the building where Hasina was present, it said.
In retaliation, police officials stationed at the premises opened fire at the attackers but they fled the spot, the report said.
Two cases were lodged and charge sheets naming 16 people filed in February 1997. In July 2009, charges were framed against the accused.
Leaders of the ruling Awami League have in the past said that assailants have made attempts on Hasina's life at least 19 times since the killing of Bangabandhu.
In August, 10 people were sentenced to death in one of the Hasina assassination bid cases.