Scottish Origins of the McAskies

Scottish Flag

McCaskies in Scotland

The McAskies were Celts with Viking thrown in, originally part of Clan MacLeod of Lewis

The Clan MacLeod

The forefather of the MacLeod's was Leod, a son of Olaf the Black, the last Norse King of the Isles. Leod inherited the  Isles of Lewis and Harris and parts of Skye in 1237. The family later acquired Dunvegan Castle through marriage, which still remains in the family.  Lewis was given to Torquil by his father, Leod of Norway descent. Torquil became MacLeod of Lewis.The MacLeods of Lewis are descended from Leod's son Torquil.

MacAskey, MacAskie, MacCaskie were all members of the Sept of Lewis

Septs of Lewis:-
Askey, Askie, Aulay, Callam, Callum, Caskey, Caskie, Challum, Lewis, MacAbe, MacAllom, MacAllum, MacAsgill, MacAskey, MacAskie, MacAskill, MacAulay, MacCabe, MacCalim, MacCallam, MacCallum, MacCaskill, MacCalume, MacCaskell, MacCaskie, MacCaybe, MacClure, MacCorkindale, MacCorquodale, MacCorkill, MacCorkle, MacGilliechallum, MacKaskill, MacKorkill, MacKorkle, MacLewis, Malcolmson, Norie, Norrie, Norry, Nory, Tolmie

Septs
 Essentially, a clan is a collection of families, living in a more or less defined area, and loyal to a specific chief.  The most powerful family (which is also usually the wealthiest) carries the name of the clan - in our case, the MacLeods. 

Other families that belong to the clan are referred to as "septs.

From George Black's The Surnames of Scotland - Their Origin, Meaning and History

Badge of the
Clan MacLeod

MacLeod of Lewis Tartan

Badge of the
MacLeods of Lewis

Isle of Harris

Later McCaskies came down to the lowlands -
see references below to Dumbarton & Glasgow areas:-

Askey/ MacAskey/ MacAskie/ MacCaskie

A Galloway surname. G. MacAscaidh, 'son of Ascaidh,' a pet form of Askell.

Thom McKasky was one of the workmen engaged in "the byggen of the kyngis rowbarge byggyte in Dunbretane" in 1494 (ALHT., i, p. 24N).

Thomas Makcasky was reidare at Glasfurde, 1574 (RMR.)

Thomas M'Caskie was admitted burgess freeman of Glasgow, 1588 (Burgesses).

I assume that our McAskies came from the West Coast of Scotland -
Galloway or Ayrshire - as many Ulster settlers came from there, but it has not been proven.