See the main entry. The vowel change to ㅏ(a) is irregular; Ko Gwang-mo believes it was potentially influenced by a putative suffix *갓(-*gat-), which would have been the yang-vowel form of the etymologically unrelated Early Modern suffix 것(-geot-).[1]
Northern and western Gyeonggi and western Gangwon form of 겠(-get-, “will, intend, probably”).
2009 February 19, 민영철 [minyeongcheol], “도읍이 되지 못한 봉성산 [do'eubi doeji mothan bongseongsan]”, in 한국구비문학대계 [han'gukgubimunhakdaegye][1], 경기도 김포시 하성면 [gyeonggido gimposi haseongmyeon]:
Sometimes the synonymous suffix 갓(-gat-), the form used in Hwanghae, Pyong'an, and Yukjin, is also written as 갔(-gat-) under influence from the standard orthography.
^ 고광모 (Ko Gwang-mo) (2007) “방언들의 미정법 어미 '겄, 갔'의 형성에 대하여 [bang'eondeurui mijeongbeop eomi -geot-, -gat- ui hyeongseong'e daehayeo, The development of the presumptive prefinal ending -keyss- and -kass- in Korean Dialects]”, in Eoneohak, volume 49, pages 165—180