Dracontia - The Serpent's Stone
First attested in Pliny the Elder's Natural History, the dracontia (aka. draconite/drakonite/dragonite) is purported to be a stone taken from the head of a living dragon; otherwise "out of spite" the dracontia will not solidify into a gem. While Pliny and select other authors describe the dracontia as a white, semi-transparent gem, other accounts describe it as being beautifully colored. It has had various powers attributed to it, or even none at all (Pliny), but the most commonly believed is that of detecting and curing poisons. Semi-related is the Adder Stone (also known as hag/witch/holey stones, anguinum, Glain Neidr in Wales, and Hühnergötter in Germany), a glassy stone (usually flint) with a naturally-occuring hole which, in addition to curing poison/snake bite, also allows one to see through glamours, win lawsuits, and has protective properties. It was so named because it was thought to be created by the saliva of several congregated serpents (once again from Pliny), though some accounts also claim that it comes from the head of a serpent (just like dracontias) or is the result of an adder "stinging" the rock.
Whereas in the 17th to 18th century, British antiquarians William Stukeley and John Bathurst Deane used the term 'dracontia/dracontium' to refer to sites of purported "ancient serpent worship", particularly locations of standing stones or pillars such as those found through the British isles. One notable example is Abury.
The dracontia has even been used in various media, not the least of which is the "dragon/dragoon spirits" in the PS1 game The Legend of Dragoon (my dearest heart).
Similarly, some stories and games see crystals in place of a dragon's heart. Labradorite has come to be known as "dragon heart stone" in some practices (wish I knew where this originated and when).
Any way you look at it, even without talking about dragons' supposed propensity for hoarding gold and gems, there seems to be a frequent association between dragons/serpents and rocks. Or maybe there's just a rock for everything. Even in the actual mineral kingdom, there are several specimens named for or associated with dragons/serpents: serpentine, septarian (aka "dragon stone"), dragon's blood jasper (technically green and red epidote, also also called dragon stone), snake skin agate, dragon vein agate, among others.
Given that you can't really go out and harvest a mythical dracontia, and it would be bad form to try anyway as someone who wants to work with dragons, your next best bet would be to choose a stone you can dedicate to your dragon workings.
Why have a dedicated dragon stone?
-Energetic battery. If your paradigm deals with it, you and/or your draconic allies can charge the stone with draconic energy, which you can tap into to get yourself into a good mindset for dragon work, and could be used to give your working extra "oomph".
-Magical focus/conduit. Even without a stored energetic component, the built-up draconic association you make with it can allow it to act as a channel or an anchor. One idea, for those who work with elemental aspects, is to have a dracontia for each associated element/group of elemental dragons that they can use as a physical representation in ritual. You can honestly be pretty creative with this.
-Symbol of your path. Whether you only have one stone or many in your practice(if any), it can be considered not just an important tool, but also represent dedication to your draconic path. You might call it a "spiritual investment piece". It can also be useful for on-the-go workings or in situations where having a physical altar is not an option.
But what stone should/could I use?
Any, really. If you want to go super obvious and use one of the aforementioned serpent/dragon-named stones, that's fine. Is there a different stone that feels more dragony to you? Go for it. Want to follow dracontia lore and use a milky quartz? Sure. My first one was a Botswana agate that looked like a grey and black dragon eye from one side, so any stone that looks like a dragon's eye would also be great. It boils down to your personal association, unless you have dragon allies giving you a particular suggestion. It doesn't have to be a fancy expensive stone, or even a new stone; if you already have some sort of stone collection, you might have something suitable. Or you might be able to find an interesting quartz-streaked river rock from a local natural area.
As an aside, if you have some ability to sense spirits/entities, you might come across a stone that seems to have a dragon attached to it. I don't mean in the "spirit binding/keeping" sense, just that a passing dragon found the stone and went "mine!" and is sticking with it. While you might be able to use the stone as a dracontia, you'd have to take it up with the attached dragon first. It might be that you'll have to pick another stone, while the stone with the attachment would only be used for working with that specific dragon. I have a tektite with this kind of thing going on.
What if I lose my dragon stone?
Then you'll just have to find another and start over with building your association with it. There's no magical consequence or punishment. If there was an attachment, it may be that the dragon has moved on. Some may feel that it could be a message that it isn't the right time for you to be following this path, that the stone wasn't right, or any number of worries, but that kind of thing is for you to discern. Sometimes you just lose things.
Do I have to call it dracontia? And do I have to have one to work with dragons?
The answer to both of these is 'no'. Some might be put off by the lore of the dracontia due to the whole "dragon killing" thing, which is understandable, and is why I mentioned the secondary use of the term in reference to temple standing stones, even if it's a relatively more recent usage, along with other variations of the concept. As long as the mythical origin of attainment isn’t what you focus on, it’s unlikely that the dragons you work with will be offended, considering it’s not how you’re getting your dragon stone anyway.
I also do not personally know of an existing dragon path that utilizes a similar concept (not to say there aren't any, I just have never heard of it in a modern dragon magic context), and decided to write about it as something that had come up organically in the early stages of my own path. So, if you've been thinking about doing something similar on your path but weren't sure about there being any precedent or are afraid of doing something silly or 'wrong', here's encouragement to go ahead and try it out.
And honestly, you don't technically need to use a stone for this purpose; a favored dragon pendant or other jewelry can be used for the same thing, I just decided to write about the 'dragon stone' in particular for the historic associations and potential interest to others who may not have come across the idea before.
As to how you would use your dragon stone… Well, that would largely be up to you. You could meditate with it, using it as a focus to facilitate connection with the dragons you work with or as a point of contact with dragon energy. You can keep it on your dragon altar if you have one and use it as a conduit/portal. Carry it with you during the day for when you need a boost or need to fuel a dragon-flavored shield. The limit for how you can use a dragon stone and what for is really just limited by your imagination and the techniques you know.
For me personally, the first dragon stone I had (the Botswana agate) was a symbol of my draconity foremost. I would hold it when I felt I needed comfort or protection, or wanted to feel dragony. I ended up losing the stone (along with some other favorite stones I still sorely miss) the last day of fourth grade, but that's how I can confidently say that losing your dragon stone isn't going to harm you. I also never took it as a message of "this isn't for you", as I continued having interactions with dragons and further exploring my draconity well after that. It's a tool in the end, despite how much meaning you might put into it.
References
Jennings, Hargrave. Ophiolatreia. London, 1889. Sacred-texts, https://www.sacred-texts.com/etc/oph/index.htm
Pliny the Elder. The Natural History of Pliny, Volume 6. July 19, 2020. Project Gutenberg, https://www.gutenberg.org/cache/epub/62704/pg62704-images.html
Deane, John Bathurst. Dracontia, or Observations on circle and serpent worship. London, 1834. Hathi Trust, https://catalog.hathitrust.org/Record/009724090
https://en.wikipedia.org/wiki/Adder_stone