There are two major theories to explain where the people from Galatian must have come from:

Northen theory:

Some scholars like  J. B. Lightfoot identifies the Galatian people with the Celts or Gauls who moved across Italy, Macedonia, and Thessaly to the coast of the Hellespont across the sea into Asia Minor where they put the whole continent west of Taurus under tribute only to be defeated by Pergamene, placed into a strip of land 200 miles long from the northeast to the northwest and to establish three cities: Tavium, Ancyra, and Pessinus4

Southern Theory:

Even though there was a unanimous northern position until the eighteenth century, it may be explained by a common error made by the church fathers which was continued by the commentators

Other scholars points out that in AD 37 Lycaonia Galatia was detached and united with Cilicia and Isaurica to form an enlarged province of Cilicia, and in 297 the remainder of south Galatia, with some adjoining territories, became a new province of Pisidia with the Pisidean Antioch as its capital and Iconium as its second city