Hi Chris,
I see you have been searching for information relating to your William Aldworth Clarke for many years!
The first thing I noticed about your post is - you say you know most of the children of William Clarke and Anne Fogarty born around the 1760s and you are looking for another son of William & Anne born around 1791-1793 do you not think it would be a little unusual if they had another child 30 years after William, Sylverster, Frederick & Henry??? How sure are you that William C. & Anne F are his parents?
I have a book on the records of St.Finbarre's Cathedral edited by Alicia St. Leger & published by The Representative Church Body library ( Church of Ireland) for the years 1753 - 1804.
I did go through all of the Clarke/Clark/Clerke entries and there were 43 in total.
I have written them all out but am just going to list some that may be relevant to your Clarkes -
Births
23 Mar 1788 Mary dau of Samuel & Eliz Clarke
****** 3rd Sept 1793 William son of Frederick and Eliza Clarke
(maybe this is the William you are searching for) a son of Frederick possibly born 1760s rather than a brother???)
12 Sept 1798 Thomas son of Thomas C & Martha Clarke
DEATHS -
****** 14th July 1773 Mr. Will. Clark, Burgess
****** 25 Feb 1786 Mrs. Anne Clarke - Newspaper notice "died yesterday morning at Crosses Green, Mrs. Anne Clark wife of Mr. William Clark of this city, merchant"
****** 23 Feb 1787 Wm. Clarke
****** 15 April 1792 Mr. Silverter Clarke
2 Sept 1793 Eleanor Clarke
Marriages -
CLARKE
9 Jan 1768 Edward Clarke, woolcomber & Eliz.Naile
17 Jan 1785 Robert Wallis & Eliz. Clarke
2 Sept 1786 John Clarke & Eliz. Fowkes
27 Aug 1792 Benj. clarke & Anne Knight widow
22 May 1793 John Condon & Eliz. Clarke
28 Apr 1797 Jerim. Clarke & Mary Corr
17 Dec 1804 Wm. Clarke farmer to Agnes Walsh both from Bandon, Co. Cork
Clerk-
24th Sept 1800 Jno. Clerk & Bridget Gillman
Clark
24 Sept 1800 Robert Clark tanner to Rebecca Gillman
No marriage for William Clarke & Anne Fogarty and no births for this couple.
You mentioned that the Clarkes of Crosses Green would have attended St. Finbarres Cathedral but
Holy Trinity Church -known as Christchurch was very near to Crosses Green so they may have had all of their children baptised there. That is located where South Main Street is now.
I have a book of records for Christchurch but only for the 1600s which is too early for you.
I have some newspaper extracts from Rosemary Ffolliot's newspaper extracts available on microfiche at the Cork City Library local studies section - unfortunately due to "Cut Backs" the local studies section is not open to the public on Mondays or Tuesdays.
A few extracts -
24 Sept. 1806 marriage - yesterday morning at St. Peters church by the Rev. Archdeacon Thompson, the Rev Thomas Walker to Miss Clarke dau of William Clarke Esq and sister to Major General Sir William Clarke Bart.(MLB Anne Clarke) ** Note she married in St. Peters church which is in South Main Street Cork .
18 May 1812 marriage yesterday morning at St. Finn Barrys ( St. Finbarres Cathedral C of I) by the Rev. H.T. Newman, Mr. Michael Pearse to Miss Catherine Clarke dau of the late Silvester Clarke Esq. of this City,
Marriage 12 April 1773 this morning at Christchurch Mr. Abraham Clark to Mis Elizabeth Searls
Marriage 8 Feb 1820 on Friday last at Passage Church Co. Cork the Rev Francis M'Leland, Chaplain to the Settlers proceeding to the Cape of Good Hope, to Elizabeth 2nd dau of Frederick Clarke Esq. of Passage and niece to the late Major General Sir William Clarke Bart.
Marriage 12 June 1800 lately at Madras, Sir William Clarke to Miss Margaret Prendergast
8 Oct 1823
Death 8 Oct 1823 at his seat, Petersfield Co. Tipperary, Samuel Prendergast Esq., late Crown solicitor for the Munster circuit and uncle to Sir William Clarke Bart. ( Could Margaret above be this
man's daughter??)
Marriage 6 Sept 1827 on Tuesday 4th inst. by the Rev Charles Leslie at Douglas Church, Sir William Henry Clarke Bart., to Elizabeth Barbara only child of John Moore Travers Esq., of Clifton near Cork.
That's it hope you can find something useful in the above.
I think the William Clarke born 3rd Sept 1793 looks like a good possibility for the William you are searching for?

Mary
Celtic Liberty