There's no record of King James the First of Scotland throwing anyone out, he had a very eventful life though and ended up being murdered in 1437 CE.
King James the First of England was later but still doesn't have any record of throwing Scots out of Scotland.
I'm pretty sure exile was common enough, during that time period, and I assume @Xue Sheng is referring to something of that sort, on a more individual basis, rather than some sweeping banishment of an entire group.