Given Padmé's extensive legacy and the many stories featuring her, it's easy to forget that her identity as Queen Amidala was once a secret from the audience, Anakin Skywalker, and many other characters that aren't revealed until roughly an hour and forty minutes into The Phantom Menace.
After Padmé steps forward and reveals to Boss Nass and everyone present that she is Queen Amidala, Jedi Master Qui-Gon Jinn turns to Padawan Obi-Wan Kenobi and smirks, implying that Qui-Gon figured out the truth long before this revelation. This was later confirmed in the 2019 novel Queen's Shadow by E.K. Johnston.
Queen's Shadow takes place four years after The Phantom Menace as Padmé transitions from being Naboo's queen to its senator. The story is told from the perspectives of Padmé and many of her loyal handmaidens who continue to serve her, including Sabé, who spent much of The Phantom Menace disguised as Queen Amidala.
During a scene in the novel where Sabé is disguised as Senator Amidala, Senator Bail Organa realizes the deception. There is no harm done because it is in this story that Bail becomes a close friend and ally to Padmé. She confides in Bail that he is "in select company." Read the rest of the relevant excerpts below:
"Only a few people know the full lengths my most loyal bodyguards can go to, and only one other person has ever figured it out on their own while we were in the middle of a deception."E.K. Johnston
"'His name was Qui-Gon Jinn,' Padmé said. As always, a feeling of almost overwhelming sadness threatened her when she thought of him. He had been patient and understanding of her, never asking for more than she was willing to give, and he had given all, in the end."E.K. Johnston
Qui-Gon could see that there were larger forces at work behind the Trade Federation's invasion and that young Anakin was the Chosen One, so it's no surprise that he also figured out the truth about Padmé on his own. However, it's nonetheless satisfying to have the confirmation. It's also touching to hear how much Qui-Gon still means to her, even four years after his death.
When Qui-Gon first meets Padmé in The Phantom Menace, she is disguised as a handmaiden, and Sabé is the one presenting herself as Queen Amidala. Qui-Gon and Obi-Wan save them and the rest of their royal retinue as they are being taken to a Trade Federation prison camp by a squad of B-1 battle droids.
Shortly after this, Qui-Gon addresses Sabé as "Your Highness" in the Theed Hangar and urges her to come with him to Coruscant. As Sabé seemingly weighs her decision, she looks at one of her handmaidens, Padmé, who replies, "We are brave, Your Highness," essentially giving her approval to leave with the Jedi.
Between this and Padmé saying in Queen's Shadow that it was during one of these deceptions that Qui-Gon figured it out, it seems that Qui-Gon knew the truth the entire time. When rewatching The Phantom Menace, this adds another layer to many of his interactions with Padmé, especially during their time together on Tatooine.
When Captain Quarsh Panaka tells Qui-Gon that Queen Amidala has commanded her handmaiden, Padmé, to accompany him in the Mos Eisley spaceport, Qui-Gon questions the decision but accepts it. He commits to maintaining the ruse on Tatooine, Coruscant, and Naboo, never doing or saying anything that would undermine the careful system of decoys and bodyguards that had been created.
Before the Boonta Eve Podrace, Padmé says to Qui-Gon, "You Jedi are far too reckless. The queen is not –" and Qui-Gon cuts her off and says, "The queen trusts my judgment, young handmaiden. You should too," to which Padmé retorts, "You assume too much." This exchange is one of several that are more meaningful with confirmation of what both Qui-Gon and Padmé know.
One of the many rewarding aspects of Star Wars books is that they further enrich the movies. Queen's Shadow makes Qui-Gon and Padmé's dynamic in The Phantom Menace compelling in new ways 25 years after the prequel was first released.