Fans know that when Roger was mistaken for being Brianna's rapist, he was sold off by Young Ian and Jamie to the Mohawk. The Mohawk kept him captive for months until finally he was rescued by Jamie, Claire, and Young Ian who sacrificed himself for Bree and Roger's sake.
Roger volunteers for this dangerous mission perhaps in large part to prove himself to Jamie Fraser, to prove to his father-in-law that he is fit to be a captain in the militia. Of course that all goes terribly wrong and he is “accidentally” hanged by Governor Tryon, after being mistaken for one of the Regulators.
He was subsequently hanged by the British army and fans believed he was dead when Brianna Fraser (Sophie Skelton) discovered his limp body. Fortunately, Roger survived the ordeal but he struggled in the aftermath as he lost his voice and could not forget how close to death he had come in Outlander season five.
As Roger tries to sing again, he ends up with all the memories of being hanged. In the series, Roger has got his voice back.
“There's not quite as much in the book to play with, so that is why we decided to use the ether as a method of her trying to cope,” Davis said. “For Claire, the ether is not addictive in itself, but the feeling it gives you is.
On his own journey into the past, Roger encounters his ancestors William and Morag, who take ship from Scotland to America with their infant son, Jeremiah.
Roger is a descendant of Geillis and Dougal's son. Roger has Geillis's green eyes and inherited her ability to pass through the stones. He meets her in 1739, having traveled through time in search of his son, Jem.
Roger (played by Richard Rankin) was wrongfully hanged at the Battle of Alamance and despite being rescued by Claire Fraser (Caitriona Balfe), he lost his voice and was unable to sing to his son Jemmy.
"I think that Jamie found the respect for Roger. There was a lot of misunderstanding between the two of them from the off, but he's seen him in the light of what he is and has a respect and admiration for Roger, which will presumably continue from here on in."
Rayleigh reveals that Roger turned himself in to the Marines. The reason as for why Roger turned himself to the Marines was because four years prior his death, Roger came down with an incurable disease.
Bree proceeds to tell everyone that Jamie beat up Roger because of Lizzie's error, and Claire calls out Jamie for lying that his injured hand was from making whiskey.
Apparently, the stones realized that Brianna and Roger weren't ready to leave the 18th century just yet. They both said they'd wished to go "home" as the stones whisked them away, and that's exactly where they went: the place they now consider to be home, back with Jamie and Claire.
Geillis is presumed dead after being burned at the stake, but not before Claire notices her smallpox vaccination scar, thereby revealing that she is a time traveler, too. Until the whole witch-burning incident, in which Claire is almost a victim herself, she has a love-hate relationship with Geillis.
In Scotland in 1968, Claire tells Roger Wakefield that Geillis Duncan was his ancestor and that she was burned as a witch in 1743.
During Outlander Season 3, we learn that Murtagh survived. Not all the details are shared, but somehow, Murtagh ended up being captured and was at Ardsmuir with Jamie. He's then transported to the colonies with everyone else except Jamie. When Jamie eventually gets to the colonies, Murtagh is there in North Carolina.
They settle in 20th century Lallybroch, following along somewhat with what Claire and Jamie are up to in the 18th century by reading a series of letters from Claire to Jamie.
As Ian grieved, he was told to leave the Mohawk tribe. They believed the man's spirit must battle with the woman's and overcome it, but sadly, the Mohawk tribe felt Ian's spirit was not strong enough for a child to take root in the womb and therefore, he and Emily were no longer compatible.
Roger and Brianna are distantly related in Outlander
Brianna is the child of Claire and Jamie. Jamie is Dougal's nephew. This is important to remember as it does mean that Brianna and Roger are both related to Dougal MacKenzie. Roger is not the son of Geillis and Dougal.
Some think Jamie's spirit (but not his body) traveled to through time to guide Claire to him; others suggest Jamie had a near-death experience after the Battle of Culloden, and that's why his ghost is 25 when he appears to Frank.
Geillis Duncan was tortured with the pilliwinkes on her fingers and by binding or winching her head with a cord or roape.
William Buccleigh MacKenzie is the illegitimate son of Dougal MacKenzie and Geillis Duncan, and was raised by William John and Sarah MacKenzie.
The mysterious Master Raymond is a "prehistoric time traveler." Not much is known about him, but he is thought to be a common ancestor of both Claire Fraser and Geillis Duncan.
Only if the other Outlander theories are right
It's possible that Amelie's sister is the one who gives birth to the line that leads to Claire. Fergus will still be an ancestor but not a direct ancestor and that would mean Laoghaire isn't one of Claire's ancestor.
The simple answer is no. Claire and Jamie don't have any more children after Brianna. Claire heads through the stones while pregnant with Brianna at the end of the second season/book. She spends 20 years in the 20th century, and she and Frank don't have any children together.