The only known reference to the existence of a Francis Skinner is his membership in the Woodbridge Presbyterian Church in 1708. (church-a) Other references to Francis, as shown above, are sheer speculation not supported by any records.
Francis Skinner, as well as Deacon Richard Skinner and John Skinner, was a member of the First Presbyterian Church of Woodbridge. As discussed elsewhere, I assume all three to be brothers, and likely children of first-generation Richard Skinner and wife, Susannah Poulain.
Nothing more is known about Francis, though one can speculate about his potential children. Two brothers, Nathaniel Skinner, Senior and Cornelius, Senior appear in Somerset County, NJ in the 1730's. Nathaniel's tombstone records that he was born in 1705 or 1706 at Woodbridge. This connects Nathaniel and Cornelius to the Woodbridge Skinner family - Deacon Richard, John and Francis. Nathaniel and Cornelius would likely be sons or grandsons of one of those three Woodbridge Skinners.
The offspring of John Skinner are well-documented. They do not include Nathaniel or Cornelius.
Nathaniel and Cornelius could have been the sons or grandsons of Deacon Richard Skinner. What little is known about Deacon Richard is somewhat confusing. According to his tombstone inscription, he would have been born in 1664 - before his presumed parents came to New Jersey and before his presumed parents were married here. As discussed elsewhere, I presume that the Deacon had two children - Richard Jr. and Wright Skinner. Richard Jr. is clearly referred to as 'Junior' in the records and could only be a son of Deacon Richard. I presume Wright to be a son of Deacon Richard by virtue of Wright's first name - the Deacon having married into the Wright family. Richard, Jr. and Wright served together in Thomas Ffarmer's 1715 regiment, along with another third-generation Skinner - cousin John Jr.
Wright Skinner lived near Nathaniel and Cornelius in Somerset Co., NJ during the 1730's and 1740's. A Somerset County storekeeper, Jacob Janeway, recorded deliveries and payments involving Nathaniel, Cornelius and Wright Skinner. Janeway often recorded family relationships in his notes, including the fact that Nathaniel and Cornelius were both brothers-in-law to Benjamin Manning. However, Janeway never recorded any relationship between Wright Skinner and the two brothers - Nathaniel and Cornelius. In fact, there is one entry of the storekeeper in which Cornelius and Wright Skinner are both mentioned. In that entry, the storekeeper mentioned that Cornelius was brother-in-law to Ben Manning, but goes on to mention Wright Skinner without indicating any relationship to others. I conclude that Nathaniel and Cornelius were not brothers to Wright Skinner nor sons of Wright Skinner's presumed father - Deacon Richard.
Nathaniel's birth year of 1705 or 1706 is also awkward in terms of Nathaniel being a son of Deacon Richard. The Deacon was born in 1664 - Nathaniel would have been somewhat young to be a son. The Deacon's presumed children - Richard Jr. and Wright, were old enought to have served in Ffarmer's 1715 regiment. Nathaniel seems to be a half generation younger than them.
This leaves Francis Skinner as being the best candidate to be the father of Nathaniel and Cornelius. Lester Holcombe (Holcombe-2) speculated that Francis was the father. If true, the relocation of Francis to the relatively unpopulated regions of Somerset Co., NJ with sons Nathaniel and Cornelius would help to explain Francis' absence from NJ records.
Nathaniel and Cornelius could just as easily be the sons or grandsons of an unrecorded brother of John, Deacon Richard and Francis. I tend to believe, however, that a Skinner who fathered Nathaniel in Woodbridge in 1705 or 1706 would have been appeared in some type of local record.
I presume that Nathaniel and Cornelius had other siblings, including Susannah, Richard, Robert and Phinehas Skinner, who could also be children of Francis.
Exhibit a - "Session and Trustee Records of the First Presbyterian Church of Woodbridge, NJ", Presbyterian Church Library, Phila, PA, Vault BX9211.N57095 F51, Vol I, 9/14/1995/KDS:
(KDS note - Volume I is deteriorated, though I had no problem reading the following names; Volume II is a handwritten copy of Vol I which is much more legible, but which may contain transcribing errors; both are also available on microfilm at this library and via the LDS library system.).
"The names of the Church are as follows: [KDS note - there were 20-30 names listed in total]
June 8, 1708 - Francis Skinner
[KDS note - this is the only document I know of that indicates the existence of a 'Francis Skinner'; Note also that the 'i' in Francis is clearly dotted in the original Vol. 1 record. It is Francis (him), not Frances (her).]
Exhibit 2a - "History of Perth Amboy, NJ", by William A. Whitehead, p387, per notes of DSW/VEM:
"Francis Skinner - b. 1671
Ann Skinner - b. 1673"
[KDS note - Whitehead lists no birth dates in his book - must be unsourced DSW/VEM notes; Page 387 is the widely published list of the members of The First Presbyterian Church of Woodbridge, which includes Francis and Ann Skinner, Ann being the probable wife of John Skinner. Those birth dates are someone's guess, probably from the records of the LDS library system where there are many speculative dates. Genealogists always assume children are born two years apart.]
Exhibit 2b - "Descendants of Richard Alexander Skinner of Loudoun County, VA", by Lester Granville Holcombe, 1972, 10/26/1995/KDS; available at the Church of Latter Day Saints library system, microfilm #1421466.
"Third child of Richard and Susanna Skinner was Francis Skinner, born circa 1672; m. 1702. Francis Skinner was received into Church of Christ (Presbyterian), Woodbridge, N.J. on June 6, 1708. Note--Church members at Woodbridge under the pastorate of Rev. Nathaniel Wade, 1707-1710. From Monnette's "First Settlers", p. 112, are listed four children for Francis Skinner:
Richard Skinner 2-28-1708
Francis Skinner 6-6-1708
John Skinner 8-20-1708
Ann Skinner 8-20-1708"
[KDS note - Holcombe is in error. There is no information to suggest that Francis is necessarily the third child of Richard and Susannah. And Holcombe's interpretation of Monnette is also in error. Monnette never lists children for Francis. Page 112 of Monnette, referenced above by Holcombe, is the widely published list of the members of The First Presbyterian Church of Woodbridge and their date of formal church membership. Monnette never suggested that those individuals were children of Francis. In addition, note Holcombe mis-copied some of the church membership dates, making the above list useless. Also note that the marriage date for Francis is probably sheer speculation not supported by any records.