The boy suffered serious burns to his face and arm at a Home Bargains store in Worcester on 21 July.
His 39-year-old father, who cannot be named for legal reasons, pleaded not guilty to conspiring to commit grievous bodily harm when he appeared at Worcester Crown Court on Tuesday.
Five other men and a woman denied the same charge during the hearing.
They are Adam Cech, 27, Jan Dudi, 25, and Martina Badlova, 22, all from Birmingham; Norbert Pulko, 22, and Saied Hussini, 41, both from London; and Jabar Paktia, 41, from Wolverhampton.
About 30 family members and friends of the defendants were in the public gallery for the hearing.
The boy was in a pushchair while out with his mother when he was allegedly targeted in the Tallow Hill area of Worcester.
He was treated in hospital and discharged the following day.
All the defendants were remanded into custody as the case was adjourned for a preliminary hearing on 21 September.