Is saying "Alhamdulillah" when a child sneezes considered an innovation (bid'ah), and is it obligatory to say it when sneezing during prayer?

Sneezing and saying "Alhamdulillah" (praise be to Allah) is one of the confirmed Islamic manners. If one does not praise Allah, then one should not respond, based on the hadith: "This one praised Allah, and this one did not praise Allah." If a discerning child sneezes, they should be taught to say "Alhamdulillah" when they sneeze, and one should say to them, "May you be blessed," or "May Allah mend you," or "May Allah have mercy on you." There is no difference in responding to someone who praises Allah, whether they are young or old. As for a small child who has not reached the age of learning, some scholars have held that their guardian should praise Allah on their behalf. However, the more apparent view is that praise is required from the sneezes themselves. Nevertheless, if a suitable supplication is made for them, we hope there is no harm in it. And whoever sneezes during prayer is lawfully permitted to praise Allah, but they should say it silently and not out loud, for fear of disturbing the other worshippers.