the real focus of this entire thread has been trying to establish a link between John Davis and Ernest Davis.
Katorama, I hope you can somehow find that link. BUT - there are so many unknowns. John Robert Davis: you only have Ernest's word that this is his father. Did he actually know his father? Perhaps he was just told this name to appease his curiousity. Or perhaps he made up the name himself so he could move easier in the non-Chinese community.
There are about 26 John Davises (according to Vic BDM) who might be eligible by age to be Ernest's father in the period 1871-1880, including the John Davis who died in Beechworth in 1871.
My thoughts on this is you might be better off to find out more about Ernest's beginnings by doing further research on Ernest first.
Here are some links which may assist (supposing Ernest is half Chinese):
https://blogs.slv.vic.gov.au/family-matters/researching-your-chinese-victorian-ancestors/https://www.familysearch.org/en/wiki/Chinese_in_AustraliaPerhaps questions are: were Chinese births registered somewhere different to BDM, where did the Chinese born children go to school and are those records available, was there a Chinese publication for the Chinese community and also a printed directory and what can you find out in general about the Chinese camp in Beechworth (ie social practices, medical and child birth practices, attitudes to an illegitimate child (with father of different ethnicity) etc etc
Did Ernest live with a Chinese family (which might explain his language ability - school certainly wouldn't explain it) or did he live with a yet unknown Davis family or another anglo-european family - or was he reared in an orphanage?
https://www.findandconnect.gov.au/ref/vic/biogs/E000816b.htmA school admissions register might reveal a parent of his? (Your problem there might be that he didn't bear the surname Davis as a child.)