A dialectal, archaic, or Scottish English form of 'another,' used in some regional varieties of English.
From Middle English 'an other,' phonetically contracted and dialectally reduced. The 'anither' form is particularly common in Scottish and Irish English regional speech.
Languages are constantly contracted—'another' became 'anither' just like 'do not' became 'don't,' and these dialectal words are time capsules showing how speech naturally simplifies.
Complete word intelligence in one call. Free tier — 50 lookups/day.