Assuming August was born in Fredensborg Slot Parish 5. Mar 1856 his family would be:
Father: Peder/Peter Jensen 20. Jun 1824 Fredensborg Slot Parish Mariner (the war 1848-1849), later Smallholder, Bleacher (nickname “Klippen” or original ”Kleppan” after his father mariner Jens Rasmussen born in Kleppan, Stokke Parish, Vestfold County, Norway)
Mother: Ane Andersdatter 26. Aug 1819 Karlebo Parish
Siblings: Sophie Margrethe Petersen 23. Feb 1847 Grønholt Parish Edvard Anders Petersen 23. Feb 1849 Fredensborg Slot Parish Jens Oluf Pedersen 1. Jun 1851 Fredensborg Slo Parish Anders Petersen 19. Nov 1853 Fredensborg Slo Parish August Petersen 5. Mar 1856 Fredensborg Slo Parish Marie Kirstine Petersen 19. Aug 1858 Fredensborg Slo Parish Peter Petersen 7. Aug 1861 Fredensborg Slo Parish Julius Martin Petersen 26. Dec 1863 Fredensborg Slo Parish
The family lived in Fredensborg until 1875.The last confirmation record is Peter (b. 1861) from Oct 1875.The family can not be found in the 1880 census, neither as a whole nor as single persons. Assumption:They moved to Norway (part of Sweden from 1814) between 1875 and 1878.Note that in the 1880 emi- and immigration records we found, August is listed as coming from Sweden.
I found one living descendant in Denmark after Jens Rasmussen.