From: Rabbi Akiva Eiger
To: Unknown recipient
Rabbi Akiva Eiger ruled without hesitation that a dangerously ill man eating on Yom Kippur by medical necessity may receive an aliyah at the morning Torah reading, since that reading is rooted in kedushas hayom rather than the fast. He left unresolved whether the Minchah Torah reading on Yom Kippur is likewise based on kedushas hayom — permitting a non-faster to receive an aliyah — or whether it derives from the taanis institution, which would exclude one who is not fasting.
Source: Shu"t Rabbi Akiva Eiger §24