Someone supplied me with following information. I am sure it can be verified by someone with access to the referenced Documents.
From Alexander Kin II, page 323:
",,,Family tradition says that seven brothers settled in Maryland.These were ..................By some they were thought to have been sons of the Rev. JAMES ALEXANDER of Raphoe, but this has been disproven.(See Memorials of the Earl of Sterling, by the Rev. Chas. Rogers, 2 vols, publ. 1877, pp, 94-97)Rogers states that JAMES d. in 1704, leaving a will, naming only his wife.She died in 1711, leaving her estate to her niece."