I also saw that there is the word ההיא (hahí) used for “that”. I suspect this is for feminine objects instead?This is the distal demonstrative (object is far from the speaker). Its "close" counterpart is הזה [haze].
ביום הזה = on this day.
ביום ההוא = on that day.
"ביום ההוא נפלה אש מן השמים" = "on that day fire fell down from the sky."