Jacob Oxford married a girl reportedly a daughter of George and Elizabeth Lawson Rogers. His brother, Abel, married a girl reportedly named Edieth Rogers. If so, given the customs, and conditions, of the time, it's quite likely, but not certain, the two girls were members of the same Rogers family, and possibly sisters, or cousins.
I don't personally know if Jacob's wife has been solidly proven to have been a daughter of George Rogers, or if it's simply an assumption being reported as fact. I do know though attempts to connect Edieth Rogers Oxford to the family of George and Elizabeth Lawson Rogers have failed.
It's believed, and reported as certainty, that Edieth Rogers was instead the daughter of a John Rogers, who was wrongly reported to have been the Cherokee chief of that name. This report was made only by a granddaughter of Edieth, one of many, and she was trying to use a claimed descendency from this man to secure the benefits of Cherokee citizenship for herself, her children, and her grandchildren. She was joined in the attempt by several, but not all, of her brothers and sisters, and in a seperate case, but considered at the same time, by two sons of her uncle, Jacob Oxford, both also grandchildren of Edieth Rogers Oxford.
The claim of descendency from Cherokee chief, John Rogers, was quickly proven wrong. It was reported by the Cherokeethough that there was another Cherokee, also named John Rogers, a "half breed", who'd also lived in Georgia, and had been on the 1835 census of the Cherokee. With it proven these Oxford descendents weren't related to Chief John Rogers, as claimed, they then claimed they must instead be descended from the other John Rogers, and so still qualified for Cherokeee citizenship. With their first claim having been disproven, they would now have to prove their second claim.
It's evident the second claim was presented and rejected prior to 1896. Rebecca states in her request for another hearing that they'd tried "for a number of years" to be accepted as Cherokee citizens, but apparently hadn't been. They were asking that the case be heard again on the grounds "a final decision" hadn't been made by "an authorized tribunal". Another hearing was granted, and again the decision made was that the claim had to be rejected on the grounds, although it was said they were Cherokee, that there was "insufficient evidence" to prove they were descendents of the second John Rogers. This was apparently the same reason for the earlier rejection, and it was upheld after further consideration.
Rebecca Boyd Walker was eighty-five years old when she made this claim, and her affadavit shows she knew virtually nothing about her long dead grandmother's supposed Cherokee background. As follows:
1. She named her as a daughter of Chief John Rogers, and she certainly wasn't!
2. She admitted she didn't even know if she spoke the Cherokee language.
3. Her claim was based only on the erroneous belief she was the daughter of the Cherokee chief, and otherwise just the fact the Cherokee had visited her.
4. Her claim to being dsescended from the other John Rogers was based only on her belief that if she wasn't the descendent of Chief John Rogers, as she'd originally claimed, then she must be a descendent of the other man of the same name.
We can reasonably assume these Oxfords were questioned about Cherokee John Oxford to see if any of them knew anything at all that would support the claim their grandmother, and great-grandmother, Edieth Rogers Oxford, had been his daughter. Apparently, they knew nothing at all that would support the claim - just that he was Cherokee, and had the same name as they believed Edieth's father had. That wasn't enough then, and isn't enough now, to prove descendency.
We can also assume these Oxfords, obviously anxious to prove their claim, would have contacted all other family members they knew, and could reach, to see if any of them knew anything that might help them prove their case. That none of the other numerous descendents of Edieth gave supporting statements suggests all other Oxford descendents, within reach, knew no more about it than these people did, which was virtually nothing at all.
Of Abel and Edieth Oxford's nine children, none are known to have claimed Cherokee citizenship, or to have lived among the Cherokee, and seven of the nine aren't known to have passed on any knowledge of Cherokee ancestry to their children and grandchildren. The exceptions were mostly just several, but not all, of the children of Elizabeth Oxford Boyd, and only two of the several children of her brother, Jacob Oxford. The great majority of Edieth's numerous descendents made no such claim, and provided no support to those few who did.
While it can't be proven Edieth wasn't Cherokee, neither can it be proven she was. All that can be said as a matter of fact is just that a few of Edieth's many descndents claimed to be Cherokee, while the great majority didn't, but the claim of those few who did, was rejected, and certainly more than once, by the Cherokee.
Cherokee tribal leaders, and tribal members, living a hundred and eleven years ago, would certainly have known, or been able to have learned, much more about early Cherokee connections than what we can do now. They decided, and this included a man, Peter Passions, who'd personally known John Oxford, that Edieth's descendents couldn't convincingly support their claim to have been descended from him. We can't overrule their decision on nothing more than just our desire to claim a Cherokee ancestor. With that being the case, we can say only that a few of Edieths descendents, but not the majority, claimed to have Cherokreee ancestry, but thir claim was rejected by the Cherokee.