In The Wheel of Time Season 3, Mat Cauthon’s encounter with the Eelfinn, who are mysterious, fox-like beings from another dimension.
This marks a pivotal moment in his journey. This event mirrors a key sequence from Robert Jordan’s The Wheel of Time novels, on which the show is based. The Shadow Rising book depicts Mat making three wishes that profoundly impact his character and abilities. However, it can only be speculated what significance or impact these wishes will have in the series.
His three wishes revolve around fixing his memory, being free from any magical influence, and escaping Eelfinn's dimension so he can return home safely.
Read on to know about his wishes in detail.
Here's what Mat's three wishes in The Wheel of Time Season 3 could mean:

Mat wishes to have the gaps in his memory filled with useful information. In season 1, he ends up stealing a Dagger that was cursed by Shadar Logoth. Logoth is a city filled with such evil that even the Dark ones avoid going there. The dagger slowly corrupts Mat's mind and soul, leading to loss of memory and hallucinations, paranoia, and visions from past lives. Even the powerful Aes Sedai were unable to treat him fully. Therefore, in season 3, when he meets an Eelfinn, his first wish is to get his memory fixed. This gives him more clarity and freedom from a traumatic, confusing past, but useful memories from past lives in The Wheel of Time.
He has been the victim of a lot of powerful people's magical powers, such as when he was affected by the Dagger or the powers of Aes Sedai, confined in the White Tower. He desires not to be a victim of magic anymore, it had frightened him to the core. Therefore, his second wish is to be immune to these harmful magics. This will also help him in the future and change his powers and character to a significant extent. While exiting the dimension, Mat can be seen wearing a Fox head Medallion. This might be something that protects him from magic.
After navigating a terrifying, otherworldly labyrinth filled with trickster fox-beings, Mat understandably blurts out that he just wants to go home. It’s not a grand or strategic wish like the others, but it’s real. It's human. And in that moment, it might be the smartest thing he could have asked for. This wish might seem trivial, but it holds a lot of weight as Eelfinn's world is like a maze, and he can trap anyone who is not wary. Even powerful Channelers and Forsaken entered his maze but never escaped.
With the Eelfinn, everything has a cost. Since Mat asked to leave without giving anything in return, they take the price in blood. They hang him by the neck from the doorway. But that is when Min intervened and, with the help of Mat, was able to survive. Therefore, this wish further adds depth to Mat's character by making him a tougher and wiser version of himself in The Wheel of Time.