The Geni connections show Elizabeth (Rogers) Higgins and her husband Thomas Higgins having the same parents:
Parents for both are connected as Lt. Joseph Rogers, "Mayflower" Passenger and Hannah Rogers (unknown)
Thomas above also has twio wives named Elizabeth Snow who appear to be the same person. At least they both are shown as daughters of Nicholas Snow, although one has no mother connected.
I don't believe Charles Rogers is the son of the parents he's connected to. His own words state:
"Thus far, little is known of me. I am said to be the son of *Thomas and Elizabeth Rogers."
I don't believe his mother was Elizabeth Snow because the children for Elizabeth Snow are known and there is no Charles among them:
Children of Thomas Rogers and Elizabeth Snow
1. Elizabeth Rogers b. 8 Oct 1666, d. b 1704
2. Joseph Rogers+ b. 1 Feb 1667, d. 24 Apr 1696
3. Hannah Rogers+ b. 20 Mar 1669, d. b Jul 1733
4. Thomas Rogers b. 6 Mar 1670/71, d. 15 Mar 1670/71
5. Thomas Rogers+ b. 6 May 1672, d. 23 Sep 1749
6. Eleazer Rogers+ b. 30 Nov 1673, d. a 10 Dec 1739
7. Nathaniel Rogers b. 18 Jan 1675, d. b 1704
AND, more importantly, his mother was not the Elizabeth Rogers connected to him because she was his father's sister (see the Discussion on her profile) and she married Jonathan Higgins, even though at present Geni has her married to Jonathan and to her brother Thomas, which I'm hoping will be corrected.
Based on all this, I believe Charles Rogers is the son of a different Thomas Rogers altogether and that Charles mother is another Elizabeth whose maiden name is unknown. He himself didn't seem to know anything more than his parents' first names, which makes me wonder whether he was an orphan or why it is what information he had on his parents was hearsay to him and not personal knowledge of who they were.
Charles Rogers was given spurious parents - again. I suppose they could be a Thomas abs Elizabeth Rogers, but I’d like to See more data before making those profiles.
Meanwhile I’ve locked to wife Jane Rogers & unknown parents.