In addition to R-L21 and R-DF13, the Ballard Group 1 members also have a more recent SNP/Haplogroup known as R-CTS4466 that defines the Irish Type II subclade.
New GlobeTrekker BigY Migration in Ireland: https://pbase.com/daveb/image/173940951

https://www.familytreedna.com/groups/r-1b-cts4466-plus/about/background

Since this group has no direct matches to other males outside the US, we drop back and take a closer look using the advanced BigY test and related Discover Reports to see where the common male ancestors came from. In this case all YDNA signs point to early migration across Ireland after the time of R-DF13 in England. For more information see: https://pbase.com/daveb/ballard1

Research Notes: Ballard in Ireland

Ormond Deed: 373. Grant by Richard Whitesyde to Tlwmas Ballard of land in Kilbleyn. [May 19, 1403].

The deed is likely in Kilkenny: https://en.wikipedia.org/wiki/Kilbline_Castle
or perhaps Cork?
https://www.genuki.org.uk/big/irl/COR/Kilmurry

373.
Richard Whitesyde, cleric, prebendary of Kyllamerry, grants
to Thomas Ballard and his heirs all his right in ten acres of
arable land in the lordship of Kilbleyn in the field called
' carnantre ' ; which ten acres he has of the gift and enfeoffment
of John Amery and Mabine Mowyn his wife.
Given on Saturday next before the feast of St. Brendan the
abbot in the 4th year of Henry IV.
May 19, 1403. Seal.

John Ballaht grants to
Patrick Cotterell and Philip son of John Row
https://sites.rootsweb.com/~irlkik/history/cotterell.html

Two Deeds.
1) John Ballaht gives and grants to Patrick Cotterell and Philip
son of John Row all his messuages, lands, tenements, rents and
services in Insnak, Stamkarthy and Boly near Insnak, which
formerly belonged to Philip Row, grantor's ancestor.
Given on Friday next before St. Nicholas' day in the ist year
of Henry V.
December i, 1413. Seal perfect.
2) John Ballaht quit-claims to Patrick Coterell and Philip fitz
John Row all his right in all messuages, lands, tenements, rents
and services in Insnak, Stamkarthy and Boli near Insnak.
Given on Monday next before the feast of St. Nicholas in the
ist year of Henry V.
December 4, 1413. Seal perfect.

https://www.investopedia.com/articles/personal-finance/051614/five-things-know-about-quitclaim-deeds.asp
What is the purpose of a quitclaim deed?
A quitclaim deed offers the least level of buyer protection and is generally used for title transfers between family members or to clear a defect on the title. They may also be used when a property transfers ownership without being sold, that is when no money is involved.

https://en.wikipedia.org/wiki/List_of_mayors_of_Cork
1687 William Ballard James II of England also appointed Ignatius Gold. Mayor in 1690 also.
1690 William Ballard

Another source mentions that when William first held the office of mayor, King James II also appointed Ignatius Gold to serve with him. This suggests William was either allied with the Williamites or was one of the Scots-Irish (though his election in 1690 leans towards Williamite). Very briefly: the Williamites supported the protestant Prince William of Orange; the Jacobites supported the Catholic King James II in the conflict over who would be king of England, Scotland and Ireland. The result of the war is that the Protestants dominated life in Ireland, which caused discord among the majority Catholic and Scots-Irish (Presbyterian) citizens, who were excluded from power and land ownership. Wikipedia provides a good summary of the conflict. Evidently James II did not trust a protestant William Ballard and appointed a Catholic to serve as mayor with him. James was the last Catholic ruler of England Scotland and Ireland, who reigned from 1685 to 1688.

The Council Book of the Corporation of the City of Cork: From 1609 to 1643 and From 1690 to 1800, by Richard Caulfield (Guildford: J. Billings & Sons, 1876) repeatedly mentions William Ballard, Alderman. A William Ballard also served as sheriff, though the date of service is not clear from the text. However, an ancient text called The Cork Remembrancer by Anthony Edwards (1792) lists William Ballard as sheriff in 1679 (under Charles II), and notes his service as mayor in 1687 (under James II) and 1690 (under William and Mary). The appendix in the same volume includes an enumeration of protestants that fled from King James II (and includes an inventory of the value of their estates), and lists William Ballard, “w. and 8 ch.” (“wife and eight children”). One other record in The Council Book provides a clue: in one instance there is the listing of a William Ballard, Jr., Alderman, in 1694, so apparently father and son served simultaneously, and perhaps Benjamin is the son of William, Jr., which leaves a large number of William, Sr’s children unaccounted for. We have not yet found a record of direct descendants other than the snippets listed above.


https://en.wikipedia.org/wiki/History_of_Cork
https://www.rootschat.com/forum/index.php?topic=760298.0
https://ballardofvirginia.com/2013/11/17/could-bland-ballards-family-be-from-ireland/
https://ballardofvirginia.com/2015/10/06/a-possible-welsh-origin-of-lineage-group-i-a-biography-of-bland-w-ballard-of-aquilla-texas-1824-1904/

Ballard Coat of Arms & Family Crest - Symbols, Bearers, History
https://www.youtube.com/watch?v=444-SLZPuhA
https://freepages.rootsweb.com/~mturner/genealogy/cork/mayors.htm (Ballard, Sheriff & Mayor)