From a good source: It is generally believed that this branch of the Adams family trace their line to Duncan Adams, son of Alexander Adams who lived in the reign of King Robert Bruce, and had four sons: Robert, John, Reginald and Duncan, from whom all the Adams, Adamsons and Adies in Scotland are descended. The youngest son, Duncan Adams, accompanied James,Lord Douglass, in his expedition to the Holy Land with King Robert's heart, and from him is stated to have descended John Adams, who accompanied King James IV. to the field of Flodden, and there lost his life anno 1513. He had a son, Charles Adam, seated at Fanno,co. Forfar. In the middle of the 17th century there were three brothers, descendants of this family, the eldest of whom remained in Scotland, while the other two, adding an s to their patronymic, left their country; James went to Ireland, and is the ancestor of the Adams's of Northlands, co. Cavan and Monagan; and William went into North Wales, and from him sprang the Adams of Carmathanshire (now known by the name of Ap Adam) of the Adams of Pembrokeshire.
Whittemore, Henry, (1893), History of the Adams Family, New York: Willis McDonald and Co., pp. 67-68.