By studying the life of Imam Kazem (p.b.u.h.), we narrate one of the reguments of Imam with Haroon Alrashid (one of the Abbasid Caliphs):

One day, Haroon Alrashid told to Imam Kazem (p.b.u.h.): I wan to ask you something which has occupied my mind for a long time and I have not asked it from anyone so far. Meantime, I have heard that you will never lie, so I expect you to answer me truly.

Imam (p.b.u.h.) prescribed: "If I might enjoy freedom of expression, I will tell you whatever I know about your question."

He told Imam that he would enjoy freedom of expression and asked his question: Why do you and the people believe that you, the children of Aboutaleb are superior to us, the children of Abbas, while we and you are one trunk of a tree. Aboutaleb and Abbas are both uncles of prophet, so we do not make any difference considering the fact that we are relatives of prophet.

Imam Kazem (p.b.u.h.) prescribed: "We are closer to prophet (p.b.u.h.) than you; in this respect that our father Aboutaleb was the blood brother of prophet's father (p.b.u.h.) having one mother and one father, but Abbas, was not his blood brother and only they had the same mother, but not the same father.  

Harron Alrashid said: I have another question. Why do you claim that you might inherit prophet? While we know, when prophet died, his uncle, Abbas (our father) was alive, but his other uncle, Aboutaleb (your father) was not alive and it is obvious that as long as the uncle is alive, the cosine will not inherit.

Imam (p.b.u.h.) prescribed: Might I enjoy freedom of expression?

He replied: I mentioned in the beginning that you might.

Hazrat prescribed: "Imam Ali Ibn Abitaleb (p.b.u.h.) prescribed: "when there are children, except father, mother, wife, and husband, the others will not inherit, when there are children for the uncle, for which no inheritance has been proved in Koran, but not in narrations. So, those who consider uncle as father, say something and their words have no basis. It means that, when Hazrat Zahra (p.b.u.h.) is alive, as daughter of prophet (p.b.u.h.), so his uncle, Abbas shall not inherit.

Besides, prophet (p.b.u.h.) prescribed about Ali (p.b.u.h.): "Ali is the best judge you have." Also it has been narrated from Omar Ibn Khatab that he said: Ali is our best judge.

Haroon asked another question and said: Why do you let the people to attribute you to prophet? And call you children of prophet of God? While you are the children of Ali. Because everybody is attributed to his father, not to his mother, and prophet is your maternal ancestor.

Imam Mousa Kazem (p.b.u.h.) prescribed: "If prophet is alive and request you to marry your daughter, will you agree?"

He said: I take shelter to God. why not? I will be honored of that against all Arabs and non Arabs and Quraish.

Hazrat prescribed: "But, if prophet (p.b.u.h.) is alive, he will not ask to marry my daughter, and I will not agree, either."

Haroon Alrashid asked: why?

Imam (p.b.u.h.) prescribed: "because he is my father (even though he is my maternal father), but he is not your father. So, I can consider myself as the child of prophet of God (p.b.u.h.).

So, why do you consider yourself as the progeny of prophet, while one might be progeny of the son, not the daughter?

Imam (p.b.u.h.) stated: "let me not answer this question."

He said: no you shall answer and you shall prove your claim relying on Koran.

Imam Kazem (p.b.u.h.) read a sura of Koran (sura: Anam, verse: 84) and stated: now, I ask you Jesus who is called progeny of Abram in this verse, is attributed to Abram through his father, or through his mother?

He answered: as it is emphasized by Koran, Jesus had no father.

Imam (p.b.u.h.) prescribed: "So, he is called a progeny through his mother, and we are progeny of prophet through our mother, Fatemeh Zahra. Do you need if I read another verse of Koran?

He said: read.

Imam Kazem (p.b.u.h.) prescribed:"So I read to you verse: Mobaheleh, sura: Al-e Emran, verse: 61. No one has claimed that prophet (p.b.u.h.) accompanied anyone but Ali, Fatemeh, Hassan, Hossain (peace be upon them) in his argument with Nasara Najran, so in the aforesaid verse, Hassan and Hossain are proofs of "my sons" in the aforementioned verse, though they are sons of prophet through their mother and the children of one's daughter are dear".

Here, Haroon asked: do you have a request from me?

Imam (p.b.u.h.) prescribed: "No. I want to go back to my hom."

Harron said: I should think about it. (because he intended to imprison him)

Resource: Practical Tradition of Relatives of prophet (p.b.u.h.) by Seyed Kazem Arfa.