From Burke's Irish Family Records:
p427-Capt Moses Ashe of Cromwell's Army, of Ballyline, co Clare.

1659 Census of Clare
BARONY OF BUNRATTY
Parish Kilraghtis, Townland Ballylinebeg, Numbs of People 16, Tituladoes Names Moses Ash gent, English 2, Irish 14

The History and Topography of the County of Clare by James Frost
Part II. History of Thomond, Chapter 24
Book of Forfeitures and Distributions—continued
Barony of Bunratty Upper: Part A: Kilraghtis Parish
Townlands Ballylinebeg, Proprietors in 1641 Daniel, son of Loghlen O'Grady, To whom disposed of
Moses Ash; Earl of Inchiquin

The History and Topography of the County of Clare by James Frost
Part II. History of Thomond
Book of Forfeitures and Distributions: Notes
In 1659 and 1661, the tenants of the various townlands of this parish were as follows:— Ballgassane, Daniel MacNamara; Bunnahow, Thomas Butler, gent.; Cappanapeasta, Richd. Barry; Carrowkeel, Thomas Butler; Carrownacloghy, Lieut. Wm. Rosdell, and Bryan Stapleton, gent.; Doon, John MacNamara, Esq.; Derrynagleragh, Teige O’Brien; Drumumna, James Hennessy; Drumbonniv, Wm. and Robt. Denn; Knockamucky, Teige O’Brien, and Moses Ash;
In 1659 and 1661, the townlands of this parish were severally occupied by the following tenants:— Ballyline, by Thomas Butler; Ballylinebeg, by Moses Ash;

The Ashe family, like most great Norman families, came to Ireland in the 1300s. First settling in Co. Meath and Kildare, they are now chiefly found in Kerry and Antrim. They became "more Irish than the Irish themselves" and labored long and hard for Irish freedom. Thomas Ashe, the Irish patriot who died on hunger strike in 1916, makes the name revered whenever recent Irish history is discussed. The name anciently means " dweller by the ash tree" and is written in Gaelic as Aghas.

He had been a captain in Cromwell's army and settled in the townland of Ballylinebeg in the parish of Kilraghtis on 108 profitable acres.7