What about diabolic dragons?
As other answers have explained, a character could easily have both diabolic and draconic ancestry from different ancestral lines. But a character can also have diabolic and draconic ancestry from the same line.
Abishai for 5th edition are found in Mordenkainen's Tome of Foes and are antagonists in Baldur's Gate: Descent into Avernus. (I am currently playing in the latter and so am not currently at liberty to offer quotes from it, but can amend this post later once I have completed the module if someone else does not offer a more complete post.)
Abishai are draconic devils. They have the creature type of Fiend (Devil) and speak Infernal, and have all of the resistances of lesser devils. But they also speak Draconic, are physically like humanoid dragons (with wings and claw / bite attacks). They come in five colors to match the five types of evil dragons and have immunity to one damage type that matches their color. They are followers and worshippers of Tiamat, a great diabolic dragon who was once the ruler of Avernus, the first layer of the Hells.
All of the above features I have learned as a player in the Baldur's Gate module. I don't know whether their lore explains whether they are diabolic dragons or draconic devils, and I don't know whether it is possible for them to sire children with humanoids, and whether such children would be considered to have both draconic and Infernal bloodlines. But it is not a great stretch to make it so for any DM so inclined. Thus it would be possible for someone with a single Abishai ancestor to be a Tiefling sorcerer with the Dragonic bloodline. Or, for that matter, a Dragonborn sorcerer with the Infernal bloodline.