Have a look at the NRS Catalogue who have the trial listed. Different details for his father

However, he originally gave the name of Anderson and likely changed his father's name from John to James too it seems until it all unfolded and his true identity was confirmed?
AD14/35/19
Precognition against John Adam for the crime of murder at Kilcoy, Killearnan, Ross-shire
John Adam, alias Anderson, married. Son of James Anderson, farmer (deceased), Age: 31, Address: Townhead, on the estate of the Duke of Buccleuch, Origin: Native of Dalkeith
Execution referred to in Alex F Young 'The Encyclopaedia of Scottish Executions, 1750-1963', (1998), p.111.
Also
JC26/1835/126
John Adam, alias Anderson, married. Son of James Anderson, farmer (deceased), Verdict: Guilty, Sentence: Death - hanging by public executioner. Note: Case continued until 19 September 1835. Execution ordered for Friday, 16 October 1835, at Inverness. Pannel to be buried within precincts of the Tolbooth or prison of Inverness.
Monica