Hi Tony
Can't see any gaol records for him.
However he appears to have fathered a child born in 1869 -
Name Joseph Tasman Worth
Birth Date Abt 1869 at Spring Creek, Victoria
Registration Year 1869, Place Victoria, Australia
Parents: James Adolphus Worth. Annie Hearne
Registration Number 11822
Other children, registered in Victoria
18067 / 1860
WORTH, Thomas Henry
Place of event: CARL, Australia
Parents: Anne HEARNS, James Adolphus
22278 / 1862
WORTH, James Adolphus
Place of event: CARL, Australia
Parents: Anne HERNES, James Adolphus Worth
13438 / 1863
WORTH, Arthur Begbie
Place of event: FITZ, Australia
Parents: Christina BEGBIE, James Adolphus Worth
Fitzroy and Carlton are Melbourne suburbs
Victoria Government Gazette shows James A Worth, resident Ballarat, listed as a shareholder in the COURIER Al UNITED GOLD MINE dated 20 May 186
Is this the same man? Seems possible given the nature of the crimes - however, the ship is wrong (I assume from other info), and your man seems to have been in Victoria.
From Ancestry:
Tried at Sydney Supreme Criminal Court, 10 November1875
James Adolphus WORTH, aged 40; ship: Bolton; for Uttering a forged order for advertisements; Guilty; two years labour.
Newspaper mention of this
https://trove.nla.gov.au/newspaper/article/13371131? Cheers, Judith