In the comments under my last post I mentioned the Gwalchmai Light Railway, a fictional branch line near to Aberffraw.
Here is a map and 'history' I have created of the line (historical inaccuracies in italics). The red line shows the Gwalchmai Light Railway, the black line the RAF Mona extension, constructed in 1915, meanwhile the blue line is the Aberffraw Railway. The black-dash line is the Aberffraw Railway (Llangefni Extension) Act line, part of which was planned was constructed (the yellow line), except under a different Act of Parliament in 1880, after the Llangefni Scheme failed.
This was the Capel Mawr Railway, a line built similarly to the Aberffraw Railway, as its conception implemented by the Aberffraw Gabbro Company, owned by Thomas Gwyn. It was built due to the fact that Gwyn had bought a quarry for the Aberffraw Gabbro Company in 1875, in anticipation of the Llangefni Extension. It never came and the quarry industry at Capel Mawr didn't take off as quickly as Gwyn would have wanted. After a few years of slow progress, Gwyn decided to create a new scheme in 1879, called the Capel Mawr Railway, the proposal was more successful as the newly planned line would be much cheaper, so there was much more investment from Llangefni. In 1880, the Capel Mawr Railway Company received the Capel Mawr and Llangefni Railway Act, allowing the railway to be constructed. The LNWR operated the line from the outset after an agreement with Gwyn and the Aberffraw Gabbro Company.
The quarry at Capel Mawr closed in the 1880s: like that at Penrhyn, connected to the Aberffraw Railway; making the line partially redundant. However- it continued to run, but with only passenger and farm traffic to keep it going. Eventually the branch received a Parliamentary service.
The Capel Mawr branch finally gave up the ghost in 1932, as it was too expensive to run with too few passengers and goods to supply it.