The correct spelling of this phrase is beck and call. It is part of the expression “to be at someone’s beck and call,” which means “to be ready to follow someone’s orders.”
David is at the beck and call of his mother.
Beg and call is a misspelling of this phrase, but it may occasionally appear in a different context if you combine the verbs “to beg” and “to call.”
I beg and call but she doesn’t want to listen to me.
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