Draconian describes something as very strict or harsh. It comes from the Athenian lawmaker Draco, whose laws were extreme. For example, theft carried the death penalty. While it was previously capitalized, because Draco is a name, most do not capitalize it today.
It should be noted that draco is also a Latin word meaning dragon or snake. Common confusion arises with the word draconic, which originally meant pertaining to dragons, but was commandeered after Draco came onto the Athens political field. Therefore, it carries both meanings and one must use context to determine the definition.
Dragonian, on the other hand, derives from the word dragon not draco and most definitely pertains to dragons.
Below is the ngram for draconian, which has been on a steady rise for the past fifty years.
Examples
They point to Ryan’s case as a miscarriage of justice, the result of an overzealous prosecutor stretching the law and imposing a draconian sentence given Ryan’s relatively minor role in the actual crime. [Washington Times]
“The internet is the last island of free expression in Russia and these draconian regulations are clearly aimed at putting it under government control,” he added. [BBC News]
A humbled Johnson was forced to support a draconian Nixon plan sharply at odds with Thursday’s liberal idyll: the five-hour curfew. [Guardian]
That mistake got her expelled, and on Monday her school board followed a draconic zero-tolerance policy and voted unanimously to keep most of her punishment in place. [The Blaze]
I don’t think a character should just get a draconic mount, even one as limited as that of the Dragonrider, for free as a class feature. [Nerd Trek]