Steven Brust is on the record here as saying that Miklós's and Brigitta's daughter is in fact Cawti. This may explain Devera's prediction about Brigitta's unborn daughter at the end of Brokedown Palace that "everyone else will have to watch out for her".
When Brigitta announced to Miklós that she had to leave Fenario, part of the reason for her needing to leave seemed to have something to do with who her father was.
Brigitta cried out "I'm not human. I'm not elf. My father was..." — and unfortunately, left off there. In addition, one of Brigitta's internal memories is that her father would periodically "Change into his natural form" to terrorize Brigitta's mother. Also, the Demon Goddess seemed to be able to perceive what was different about Brigitta; when Brigitta confronted her, the Goddess said "You are very brave, little girl. [...] Your effort speaks well of your — lineage."
Fenario is reputedly full of demons. There is a story in Brokedown Palace that speaks of a girl losing a lover and marrying the demon that betrayed him, and in the interlude near the end, "pretty Margit" is assigned the same fate. It is implied that Brigitta is Margit's daughter ("Pretty, pretty Margit, who lost her lover in the inn where the dzur stand. Will you never learn? Your daughter will learn, won't she? But only too late. Perhaps your daughter's daughter will fare better, and some say that will justify everything.")
So the question open to speculation is, who, or rather what, was Brigitta's father?
It should be kept in mind that whoever Brigitta's father was, he is most likely Cawti's grandfather (see above) and therefore Vlad Norathar's great-grandfather.
The story seems to point to a "demon" as Margit's husband and Brigitta's father. ("She will awake in time to see Margit wed the demon...") and ("what happened to the girl?" "She married the demon."). This could be a demon in Sethra's definition (a powerful creature that can manifest in multiple places, but is subject to control of another"). There may also be some being that Fenarians (and the narrator of Brokedown Palace) would refer to as a "demon" which is distinct from all other beings that we have seen (or at least seen a definition of) in Dragaera so far.
So a "proper" demon whose true form terrorizes Margit would be possible within the mythology of Brokedown Palace (which doesn't mention the possibility of girls mating with gods, see below).
Finally, while one sense of "demon" is the looser definition of a Dragaeran living in Fenario (see below), Brigitta herself has lived in Dragaera and knows the difference between a demon and an "elf" — and she says she's not human or elf.
It's still possible that Brigitta's father was in fact a Dragaeran. Dragaerans are sometimes called "demons" (sense 2) in Fenario. In addition, Brigitta saying that she is not human nor elf might be meant as a confession of being half-and-half.
Aliera has stated that humans (Easterners) and Dragaerans cannot crossbreed, but this is something that, like the fact that Dragaerans are actually modified Homo sapiens, she may have simply gotten wrong.
At this point, arguments in the theory's favor are that Dragaerans are indeed derived from humans (and therefore should presumably have a genome that is at least similar to humans), and that a Dragaeran living in the East might have learned enough sorcery to either shape-shift or perform an illusion spell (and therefore appear to be "changing into his natural form").
Verra's sad amusement at Brigitta's bravery, and her "lineage", might imply that Brigitta's father was a Dragon, or perhaps a Dzur. Although him having been a Teckla cannot be entirely ruled out; Verra might have been expressing sarcasm.
Since we know that at least one crossbreeding between a Goddess and a Dragaeran has taken place (Aliera), it may be that a God would, for inscrutable reasons, take up with an Easterner so as to sire a crossbreed.
In addition, definition 3 of "demon" suggests that gods and demons (in the sense of entities that have learned to multilocate) are not that different.
As a possible motivation, Barlen may have done so as some sort of (jealous?) reaction to Verra taking up with Adron e'Kieron.
A much weaker possibility is Tri'nagore. In order for this to work, however, Brigitta would have to be almost two hundred years old, since Tri'nagore was banished from Dragaera 210-220 years before Brokedown Palace is set (since Tri'nagore only had the one altar near Blackchapel (in contrast to Verra's multiple altars in the Dragaeran Empire), its destruction certainly cut him off from all areas of the world of Dragaera, both in the Empire and in the East).
Since Tri'nagore did not seem to have much to do with the other of the Lords of Judgment, he does not seem to have much reason to perform such a mating.
It is possible that Brigitta's father may have been a Jenoine. This would fit in with Verra's disparagement at her "lineage", and fit in with the concept that her father had a monsterous form.
It is unclear how a Jenoine could father children with a human woman, but we know that they are skilled with genetic manipulation, and also with illusion.