We've seen canon Tevinter heraldry with two serpentine shapes entwined.

I felt a need to break it down into components and simplify for the needs of a sigil script that could be, IDK, Old Tevene.

So, we've got a dragon and a serpent - a larger, winged shape with a leg standing out, and a wingless, limbless snake. The arrowhead, placed on the left figure's wings, might represent a connection with flight and The Fade.

Tangentially (but shedding light on a connection that might be of use here), this lore post by @wyrdsistersofthedas explores how the shape of the triangle/ arrowhead in concept art and DA frescoes usually stands for the Veil or spirit essence surrounding someone.

The bent shape of the wings also reminds us of a common lightning iconography. The thunderbolt symbol is present in Thedosian lore next to the constellation Fulmenos, attributed to The Old Gods' wrath, especially in the context of the destruction of Barindur. This detail seems meaningful, because Barindur was the fourth Northern tribe mentioned in WoT, that did not join the others (Neromenian, Qarinus, Tevinter) to form the Imperium. In fact, the legends of Barindur portray the city-state as antagonistic. Its downfall is attributed to what looks like the Thedosian equivalent of Vesuvius' eruption that destroyed Pompeii, rationalized as the Tevinter Old Gods' wrath (or, later, according to the Canticle of Silence, attributed to the Magisters Sidereal falling from the Black City, which looks like a reocurrence of the same theme).

With this in mind, I'm fairly confident the Serpent represents the founding of Tevinter: three tribes united under Darinius, and the less mentioned legacy of Thalsian the First Priest of Dumat, who was also allegedly the first Dreamer. From the ancient dreamers arose the Altus class, and in the end, The Dragon came to represent them as the main bulk of mages in Tevinter, while The Serpent came to represent the Soporati -- allegorically flightless, defenseless, and doomed to slither in dirt (if we want it to be that much in their face).

I imagine Old Tevene to be an elitarian sigillic script, that's only taught to aspiring Enchanters in the Circle of Magi. Old Tevene is used for spells, the more solemn of formal documents, and, as noted by Dorian Pavus, as an embellishment in the Altus social circles.

I chose to simplify Tevinter's canon serpentine heraldry this way:

The first symbol is The Dragon -- the Altus, the second is The Serpent or the Drake -- the Soporati. The combined Imperial sigil was used in seals and spell circles during the Old God ritual era.

In modern, Andrastian Tevinter, the "wings" of the Dragon symbol are officially removed, to deprive the original sigil of its spellcasting potential and to emphasize that we no longer do the Dreamer/ Old God stuff (officially).

This sigil in Old Tevene can be further simplified in Common Script, as an acronym used in more common documents and official signatures from The Publicanium (Common for the commoners, Tevene for the Altus):

The Dragon as X,

The Serpent as Ʒ (pronounced as z or IPA Ʒ),

The combined symbol XƷ.