This is the 12V DC 1.4watt fan I want to wire up to plug into the wall. https://sun-mar.com/product/12-volt-fan/
What specification (volts,amps, watts) are required in the power supply adapter that I buy?
This was done in the cabin I have bought, but since the fan is broken and was connected to an old Casio phone power supply adapter like the following, I want to make sure I get the proper product.
Old power supply adapter
If it's honestly rated at 1.4W, 12VDC, then any 12VDC supply equal to or greater than 117mA current rating will do.
The device won't draw more than it requires for current, so a 12V 500mA (6W) or 12V 1A (12W) or 12V 5A (60W) supply would all run it just fine. Or be able to run more than one of them.
Depending on how honest the rating actually is, they might also last longer than the original supply if the rating was not quite true and the power supply was overworked (which it should not have been at 59% load.) Then again, it looks rather old indeed, and even good ones don't last forever.
The old adapter lists 12V, 200mA so I would find one that matches that. A search on Amazon should get you what you need. (Wattage isn't typically listed, but if the fan draws the full amperage, it would be 12V*200mA = 2.4W).