Is the phrase "God, appoint a deputy for me" or "My Lord, appoint a deputy for me" considered a type of polytheism (shirk)?

The meaning of the phrases "the deputizing Lord" and "the deputizing God" in the question is unclear to us. Those we inquired from the questioner's country denied their existence and stated that the phrase "Allah yanūb" (Allah deputizes) or "Rabbī yanūb" (My Lord deputizes) is said to beggars if they are not given anything, meaning "May Allah give you." This meaning does not contain any polytheism.

It seems that the questioner's issue stems from the use of "al-nā'ib" (the deputizer) for Allah Almighty. The correct understanding is that there is no harm in that, as "al-nā'ib" is one who takes the place of another. Something close to this meaning has been mentioned in the Sunnah, such as the Prophet's prayer for Abu Salamah: "O Allah, be His successor among his progeny among those who remain." This means: "Be the successor over those he leaves behind." And "khallafahu" means "he took his place in caring for his affairs." And the saying "akhlafa Allahu 'alayk" means "May Allah return to you what has been lost," and "khalafa Allahu 'alayk" means "May Allah be a successor for you over what you have lost."

The questioner should clarify his intention if his query is about something other than what has been mentioned.