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For over ten years old family research had William Parker's father as John (wife Mary Patman) son of Richard born 1808 North Carlton Lincolnshire. John shows up in Broad Lane Worksop Nottingham on UK census in 1861 and dies 18 June 1861 in Lincolnshire. John was born 1776 in Carlton Lincolnshire. John had an older son called Richard.

Father is Robert (I thought it looked like Richard on parish film) on William's marriage shown on www.freereg.org.uk to Sarah Coval (Caval on other records), but William's second son after William junior is John Richard Parker, so John here may be Richard also. 10 June 1841 (New) Sleaford, Lincolnshire, England marriage.

Other possible Willam Parker marriage 25 Jun 1839 to Sarah Foster details from record follow: place Saxilby bachelor Servant of abode Scothern with father Richard as a farmer with bride a spinster of abode Saxilby her father is Robert a farmer and witness Mary Manering.

Other aforementioned marriage to Sarah Coval details as follows: church St Denys groom William Parker as occupation carrier of abode Newark NTT and his father Robert and bride a spinster of abode Holdingham and bride's father Thomas a Publican with the witness Thomas Walster (notes by license).

William Parker on census records appears as both a farmer and a publican so he fits in well with the farmer and publican parents mentioned on both abovementioned marriage records.

I have two possibilities for William Parker's wife and three possibilities for his father including that his listed uncle Richard was his father. Is there a clear way to find the true ancestor facts with such a common family name as Parker?

Could you make this a bit more coherent -for examle as a starting point where and when was Wiliam Parker born?
Who was born 1808 North Carlton -John or Richard?
When and where were William Junior and John Richard born?

William Parker was the 1808 birth North Carlton. William junior baptised St Martins, LINCOLN, Lincolnshire, England 26Apr1840. John Richard Parker baptised MARKET RASEN Lincolnshire England 15Apr1842 who married possibly his cousin (she lived with William Parker on a UK 1861 census stated as being relation to head cousin) Mary Robson was born about 1838 ISLE OF BUTE Rothesay Scotland. The marriage was Dec quarter 1863 Lincoln volume 7a page 1012. The cousin may be a clue to who the wife of William Parker was and the Robson family name may be the husband of the sister of either Sarah Coval (Caval) or Foster.
I have a family submission of a Mary Ann Robson born 1836 in Rothesay Isle of Bute Scotland on www.familysearch.org with parents Thomas Robson and mother Anne Manning marriage 7 Feb 1831 St.michael/mount, Lincoln, England. Could this Anne Manning be a relation of the witness to Sarah Foster's marriage stated as Mary Manering? Is Manning the same family name as Manering (I remember from the television show "Dad's Army" that Captain Mainwaring was pronounced like Mannering)? Anne Manning was stated as dying 15 Motherby Ln, Lincoln, England 28 Jul 1871. The father of Mary Anne Robson, Thomas Robson, death was shown as 15 Motherby Ln, Lincoln, England 6 Nov 1872 (baptism 10 Apr 1805 St. Michael, Cambridge, England).
Furthermore, I have found a baptism of a Mary Manning 10AUG1814 in Saint Michael On The Mount, Lincoln, Lincolnshire. I have found the likely mother Anne possibility as the Ann Foster who married the possible father John Manning on 1 MAY 1798 in the church Saint Mary Magdalene, Lincoln, Lincolnshire. Is it possible that this Ann Foster is the common link that solves part of my quest?

The place of birth for both William and Sarah is North Carlton -for which the reg dist is Lincoln. The only 2 marriages I can find before 1841( when William Junior was born) of a William Parker to a Sarah in Lincoln are
Sarah Foster in 1839 (IGI has her baptised 12/11/1809 d of Rob and Mary in South Carlton)
Sarah Rook in 1838 (IGI has her baptised as Sarah Rook or Quick 12/11/1809 North Carlton)
I canr find a Sarah Coval marriage and the only baptism shows her born Swarmby

Thanks Rotals

That gives certainty to Foster over Covel and (please don't take this next bit as lecturing you) I was planning to get a large group of birth registrations once I had figured out who was really a relative and who was missing, so I did not have to go back and forth hiring registrations films (waiting for these to arrive in Australia is painfully slow and I have waited through years of arriving parish and registration films).
Also, William's likely baptism in 1807 on IGI shows the parents were Richard and Ann, but I am having trouble finding the parents' marriage. Richard was born either 1773 or 1772 in Fiskerton to either Richard and Mary (Pashley?) or William and Elizabeth Featherby (marriage 18 Jun 1771 Fiskerton Lincolshire England). Note that Richard's first four children in order are William, Ann, Elizabeth then Richard (may make William and Elizabeth slightly more likely as Richard's parents).