Shaykh Saaleh al Fawzaan may Allah preserve him and extend his lifespan said” As for the child when he sneezes then is not to be said to him ‘yarhamukallah’ ( may Allah have mercy upon you). But rather the du’aa of blessing is to be said to him; so it is said to him ‘baraakallahu feeka’ (may Allah bless you) because a child sneezed in the presence of the Prophet may peace and blessing be upon him. So, he said (to him) ‘baraakallahu feeka’ and commanded him to praise Allah
when he sneezes in order that he educates him (with this beautiful etiquette).

The hadeeth has been reported by Haafith as-Silfee in his
selection of hadeeths as it is found in the book” al kishaaf “by
Mansuur al Bahuutee volume 2 page 158.

This statement of Shaykh Saaleh al Fawzaan is found in his book “ithaaf at Tullaab” page 280

~ Abu Fajr AbdulFattaah bin Uthman