Which version have you been writing?
beckon call (wrong)
beck and call (right)
The idiom "beck and call" means to be available and ready to obey someone's orders or requests immediately. It implies being at someone's constant service or disposal. It originates from the Middle English word "beck," which means a gesture or signal, often referring to a nod or motion of the head indicating a command or request. "Call" in this context refers to a verbal summons or command.
So, being at someone's "beck and call" means being constantly attentive and available to someone's every whim or demand, being ready and willing to respond to their every gesture or command.
On the other hand, "beckon call" is an incorrect version of the idiom, likely arising from a misunderstanding or a blend of similar-sounding phrases. It's not an established or recognized idiom in English, and using it may lead to confusion or misunderstanding.