What is the authenticity of the statement: "When a servant supplicates for something, he must be certain that Allah is the one who accepts, not the verse or the narrated supplication with which he prayed, such as a supplication for relieving distress or poverty"? And how do I pray with a narrated supplication with the intention that Allah will accept my prayer? And is saying: "O Allah, for the sake of such and such, accept my prayer" invalid and considered minor shirk?

Among the etiquettes of supplication (du'a) and causes for its acceptance are that the supplicant should have a good opinion of his Lord, be certain of the answer, and have a present heart, as the Prophet (peace be upon him) said: "Supplicate to Allah while you are certain of being answered, and know that Allah does not answer the supplication of an unmindful, heedless heart."

It is preferable to supplicate with reported (ma'thur) supplications, and it is permissible to supplicate with other words as long as they do not involve aggression, or supplication for sin or breaking ties of kinship.

The phrase "O Allah, by the right of such-and-such" is a form of tawassul (seeking proximity/means). It may be permissible if the supplicant seeks means through one of Allah's attributes, and impermissible (an innovation) if he seeks means through the right of a specific person, but it is not shirk (polytheism).