The adventure Princes of the Apocalypse has guidance for adapting the adventure to the Dragonlance setting. In this section, there is a suggestion for constructing a stat block for a draconian:
There isn’t space in this book to provide stat blocks for draconians, but you can make your own by adding the half-dragon template (see the Monster Manual) to hobgoblins or lizardfolk.
The Monster Manual contains instructions for creating a half-dragon statblock. In particular, it gives the half dragon a breath weapon:
New Action: Breath Weapon. The half-dragon has the breath weapon of its dragon half. The half-dragon’s size determines how this action functions.
So if you are going to follow the guidance in Princes of the Apocalypse and the Monster Manual, draconians actually just have a traditional breath weapon. But wait! The draconian breath weapon can be expected to be different from traditional Dragonborn!
If constructed in this way, a draconian should have two different breath weapons. One corresponding to the appropriate element, and a second corresponding to the secondary breath weapon possessed only by the various types of metal dragons! These secondary breath weapons seem to be a unique feature of copper, brass, silver, gold, and bronze dragons, which the sidebar in the Player’s Handbook identifies as the Draconic origin of the draconians:
Five types of draconians, corresponding to the five types of metallic dragons, fought for Takhisis in the War of the Lance: auraks (gold), baaz (brass), bozak (bronze), kapak (copper), and sivak (silver).
For example, note the brass dragon wyrmling and it’s two breath weapons:
Fire Breath. The dragon exhales fire in an 20-foot line that is 5 feet wide. Each creature in that line must make a DC 11 Dexterity saving throw, taking 14 (4d6) fire damage on a failed save, or half as much damage on a successful one.
Sleep Breath. The dragon exhales sleep gas in a 15-foot cone. Each creature in that area must succeed on a DC 11 Constitution saving throw or fall unconscious for 1 minute. This effect ends for a creature if the creature takes damage or someone uses an action to wake it.
A brass draconian statblock or playable race created in this way should have both fire breath and sleep breath.
So while there is no unique magical ability spelled out as replacing the traditional breath weapon, a draconian constructed according to this guidance would have a secondary breath weapon that sets it apart from traditional Dragonborn.