What is the ruling on saying "in your care" or "in your father's care" or "in your mother's care"?

The ruling on saying "in your care" (fi dhimmatik) or "in your father's care" (fi dhimmat abik) varies depending on the context. If the intention is to request something and place it under someone's responsibility, then there is no harm in it. However, if the intention is to swear an oath, then it is shirk (polytheism) and not permissible, due to the saying of the Prophet (peace be upon him): "Whoever swears by other than Allah has disbelieved or committed shirk."