Oxter is from Old English and is found in several English dialects (according to Merriam Webster) though is most commonly attributed to the northern part of the island and Scotland.
It is slang for the armpit.
Specifically, it is defined as “the hollow beneath the junction of the arm and the shoulder”.
The Oxford English Dictionary notes its first use as a noun in 1420, with later use as a verb for “to lead or support by the arm”. But it hasn’t stuck around in either usage beyond regional slang.