William A. Alexander, Jr. was born about 1646, and he died in 1735.

He married Catherine Ann Liston. There was a Rev. Wm. Liston who served as a Presbyterian minister in Letterkenny, County Donegal, Ulster. His name was listed under the "Meeting of Lagan" in March of 1689. This gentleman might have been Catherine Ann Liston's father, or some other sort of a relative. See the printed page of 520 in the Appendix of the ebook link listed below:
https://archive.org/stream/ahistorypresbyt01killgoog#page/n549/mode/1up

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William A. Alexander, Jr.'s will can be found on pages 8 and 9.
https://archive.org/stream/recordsafamilyh00buttgoog#page/n38/mode/2up

Here is the book and folio information for his will:
"Will dated 3/7/1732, Somerset County, Maryland, book E. B. 9, folio 174;"
http://wc.rootsweb.ancestry.com/cgi-bin/igm.cgi?op=GET&db=david%5Fhughey&id=I3417

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William Alexander, Jr. and his wife had the following children:
William Liston Alexander (who was known as Liston);
James Alexander;
Samuel Alexander;
Moses A. Alexander;
Eliza Alexander;
Samuel Liston Alexander;
Mary Alexander; and
Agnes (Alexander) Akins.

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The item listed below from 1670, could be for the William A. Alexander, Jr., of this memorial page, or it might be for his father, William A. Alexander, Sr. This is one of the first records available, that might help to pinpoint the arrival of the "Infamous Nine" in Somerset Co, MD. Purchasing a cattle mark/brand would be a quick way to acquire a herd of cattle. Here is the quote:

"ALEXANDER, William
1670/11/09
LIV Transf. cattle mark from Thos. Stanbridge"

Link:
http://mdgenweb.org/somerset/tlis/tlis1_a.htm

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The next item is for a pledge of loyalty. In 1689, a William Alexander and a William Alexander, Jr. both signed a pledge of loyalty.

"1689/11/28
ADVL signed Advice of Loyalty; jr
ADVL signed Advice of Loyalty"

Source:
http://www.mdgenweb.org/somerset/tlis/tlis1_a.htm

Here is a copy of the oath of allegiance to King William and his wife Queen Mary in 1689, as they took over control of the Colony of Maryland, from Lord Calvert. Most of the men who signed this oath in Somerset County, MD were members of the Presbyterian church, including Wm Alexander, John Steell, and John Miller.
http://mdgenweb.org/somerset/histrec/1689.htm

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William A. Alexander, Jr. wrote out a will in 1725, and later wrote a second will in 1732 after his son James passed away early. In his will, he stated that he was a resident of Somerset Co, MD.

His will of 1732 is on the printed pages of 8 and 9 in the ebook entitled "Records of the Family of the House of Alexander", by Frances Alexander Butterworth:
https://archive.org/stream/recordsafamilyh00buttgoog#page/n38/mode/2up

In his will, he mentioned leaving some land to his sons which belonged to his father named William A. This is more evidence that his father moved to Somerset Co, MD and owned land there.

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William A. Alexander, Jr. of this memorial page, and his father William A. Alexander, Sr., bought and sold land together in Somerset Co, MD. They both signed the paperwork for numerous real estate transactions, between 1670 and 1675. Therefore they were both of adult age by the year 1670. William A. Alexander, Jr. and his son known as William Liston Alexander continued buying and selling land together, after his father (William A. Alexander, Sr.) died in 1688.

"William Alexander, prob came from Scotland before 1675, settled in Somerset County, Maryland, where he was an extensive land trader in land; He m. and had issue of record: (1) William Alexander, engaged in land deals with his father. A William, perhaps his son,, is listed as a corporal in Talbot's Co. Md. Militia in 1748. There was a large colony of Alexander's in this Eastern Shore country as early as 1665; they resided there for about a century and finally dispersed to other sections, some to Cecil County, MD."

Source:
http://wc.rootsweb.ancestry.com/cgi-bin/igm.cgi?op=GET&db=david%5Fhughey&id=I4925

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"William Alexander is mentioned on the records at Princesse Anne as one of the trustees of the Menoken Presbyterian Church." However it is not clear if this was the original William A. Alexander, Sr., or his son William A. Alexander, Jr. of this memorial page, or his son William Liston Alexander, or a different William Alexander. See page 7 in this ebook:
https://archive.org/stream/recordsafamilyh00buttgoog#page/n36/mode/2up

William A. Alexander, Jr. was said to have a grave site near the town of Manokin Hundred, where he and his father, William A. Alexander, Sr., both lived. It is unclear whether that meant that he had a grave site at the Manokin Presbyterian Churchyard, or on the family farm the near Manokin Hundred. No headstone has been found yet.

The early records of the Manokin Presbyterian Church are missing, prior to 1747. The session records for Manokin and its sister church Wicomico might have burned in a fire. Coincidentally, virtually all of the earliest Presbyterian church records in Maryland and North Carolina were accidentally destroyed in fires as well. especially around the time of the American Revolutionary War. Most of the church records were lost, and -only a few government records remain from the colonial era, to tell the tale of the "Seven Brothers and Two Sisters" Alexanders in America.

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RIP