
Correct me if I'm wrong:
About the mother: So, Ah-Duo is Jinshi's real mother, apparently Ah-Duo feels like Jinshi needs a proper protection so she plotted to exchange her child and that child is the the Empress Dowager's. That's why the chap55 young Jinshi addresses the Empress dowager "mother".
Father: In Jinshi's POV, he thinks that the former emperor is his father since he was under the Empress Dowager's care which she knows as his "mother" that makes the current emperor his "brother". But, Ah-Duo was pregnant at the age of 16-17 something so there's no way the former emperor (a pdf file) would touch her, that leaves to the current emperor who has the highest probability to be intimate with Ah-Duo.....
Conclusion: His really parents are Ah-Duo and Current emperor
Jk I still doubt it (≧∀≦) I hate how my head works

Spoiler
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So in the first season it is just the speculation of Maomao that we hear in which she thinks Ah Duo and Jinshi resemble each other - but at the same time Maomao doesn’t yet know Jinshi is royalty/a prince. It is hinted throughout the light novels that Jinshi is the son of Ah Duo and the current emperor (Ah Duo was the current emperor’s first consort/concubine basically). Maomao just found out I believe at the end of Vol 13 for certain that Jinshi is indeed Ah Duo’s son and that Ah duo spoke with the former empress and swapped their children. Though readers knew before hand too, as I believe at the end or beginning of one the novels Ah Duo has a monologue stating just that. I am pretty sure the emperor knows too and probably Jinshi does too and that’s why he was so sad when Ah Duo left her post as a consort/concubine. Just for public’s sake he is the emperor’s “brother” and will always remain so. But Jinshi does resemble the former emperor too cause he is his grandfather, which probably is confusing people now who haven’t read the light novels. Jinshi just got the looks of his mother and grandfather. Also, another interesting fact we recently found out too is that Suiren, who is Jinshi’s caretaker/lady in waiting, is actually his maternal grandmother! He is definitely surrounded by his close family.

Yeah! So, Jinshi doesn’t really find out that Ah Duo is his mother until a bit later into the novel. When Ah Duo leaves he is still unaware that she is his mother, even as of this recent chapter updates in the manga he is still unaware.
Important to note too. The Empress Dowager agreed to switch babies with Ah Duo because she couldn’t handle looking at the result of her assault of the Former Emperor. So it was a mutually beneficial baby trade. That’s also why she was able to be a bit more accepting of Jinshi/Ka Zuigetsu.

Spoiler abou Jinshi knowing the truth or not
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Until the most recent web novel chapter Jinshi still doesn't know the truth, he might have an inkling but by knowing it then he can't run away from the throne since he'll be first in line.
Maomao is the only who's been told straight away by Ah Duo about the truth

It hasn’t been explicitly said as far as I have read. But he has a good relationship with Ah Duo, so maybe. But it’s hard to tell, cause if he knew for a fact he may push Jinshi to become the heir even more, or maybe he can’t cause then it would reveal what Ah Duo and the Empress Regent did. So far only the empress regent, ah duo and Maomao know for certain. Others may speculate
I'm still confused who's Jinshi's real parents are.... Or maybe my brain just won't acknowledge it