Thad was born and raised on starships, as his parents served in Starfleet. When he began to learn about people that had homeworlds, he became intrigued by the concept. He was extremely creative and artistic, creating a fantasy world that he pretended was his homeworld, called Ardani.
From the time that he was around five years old, he would eventually invent a total of twelve languages for his fantasy world, which he shared with his sister; he wrote and developed a 300-page dictionary for at least one of his languages and taught it to the rest of his family, who sometimes used it to converse among themselves. After being diagnosed with mendaxic neurosclerosis, his family moved to Nepenthe, which became a real homeworld for him.
He was brought there because the soil had incredible regenerative properties, and it was hoped that he would get better. In theory, his condition could have been easily cured through the use of an active positronic matrix. However, due to the ban on synthetic lifeforms, there were no active synthetic matrices and no new ones could be created. In the absence of this treatment option, Thad died from his condition. (PIC: "Nepenthe")
In an Instagram story dated 5 March 2020, Michael Chabon stated that Thad was around 15 when he died, having lived with his family on Nepenthe for about 5 years at that point, meaning that his family moved there in 2391, and that Thad died in 2396. He also confirmed that Thaddeus was named after the character's paternal ancestor Thaddius Riker, depicted in the Star Trek: Voyager episode "Death Wish", and further posited that Thad may have inherited more of his mother's Betazoid ability than his sister, Kestra.
When questioned as to the creative thought process behind having Will and Deanna lose a son, Chabon explained that "it was something that arose organically on the page as the seal was broken on an imagined Troi-Riker family, allowing the passage of time, and our show's recurrent motif of loss, to flow in." 
In background notes Chabon published on 29 December 2020, he suggested Thaddeus' middle name was Worf, and that Thaddeus had died in 2396. Chabon further suggested that Thad was precocious aboard the ship, and had befriended one of the Vulcan officers. 
Thaddeus' middle name was given as Worf in the novel The Dark Veil.