"… child -- of course scaring the living bejesus out of him -- grab him …"

better to take this as a set phrase for vulgar use meaning, "to scare someone quite a lot"

I am pretty sure "bejesus' is related to "Jesus" as in the "Son of God". But it is just relatively vulgar variant of it.

This is a slang or colloquial word that doesn't really mean anything but is used for emphasis. It is found in most dictionaries. For instance, http://www.merriam-webster.com/dictionary/bejesus . Note the two pronunciations.

"Living daylights" is often used in the same way, as, "He scared the living daylights out of me."

These replace words that are/were not okay in polite conversation, especially "crap" and "shit," as, "I beat the bejesus out of him = "I beat the crap out of him" = "I beat him very severely."

dooo is exactly right. It's a "vulgar" word. It is often not appropriate to use it. Good to know the meaning of, but not to be used until your English is very good, and you know when it is appropriate. (Especially with older people; younger people _may_ not have a problem with it.)

dooo--I think it's from "by Jesus!" used to cover up some more unacceptable exclamations.

I never cared to check, so I thought it came from "big Jesus", instead of "by Jesus". :D