In مِنْ أَيَّامٍ أُخَرَ:
1. أَيَّامٍ is genitive because it follows min.
2. أُخَرَ is the adjective of «أَيَّامٍ» and agrees in case.
Why does «أُخَرَ» visibly take fatḥa? Because it is a diptote and fatḥa stands in for kasra here.
Always distinguish a word's syntactic case from its visible case marker.