Imam Ali (as) states: “Allah’s curse is on those who do not say that I am the fourth of the four caliphs.” If he is the first Imam (as) and successor and does not consider the first three usurpers of his rights as legitimate, why would he say this statement?…

Hussain ibn Zaid narrates:
Imam Jafar (asws) ibn Muhammad (asws) said, “My father told me that his father (asws) narrated, from Imam Hussain
(asws) ibn Ali (asws) who narrates from his father Ameerul Momineen (asws)who said:
“Allah’s curse is on those who do not say that I am the fourth of the four caliphs.”
So Hussain ibn Zaid said to Imam Jafar (asws) ibn Muhammad (asws), “But you say that he is the first caliph of
RasoolAllah (saw) and you do not lie.”
Imam Jafar (asws) ibn Muhammad (asws) replied: Yes. Allah says in the Qur’an:
“When Your Lord said to the angels: Verily I am going to appoint a caliph in the earth” (Sura Baqarah ayah 30).
So Adam (as) was the first caliph, and Allah says in the Qur’an, “O Dawud! Verily we have appointed you as a caliph in the earth” (Sura Saad ayah 26).
So Dawud (as) was the second caliph, and Allah says in the Qur’an,
“Musa said to Harun, be my caliph among my people, act rightly and do not follow the way of the mischief-makers.” (Sura Araaf ayah 142).
So Harun (as) was the third caliph, and Ali (asws) is the caliph of Muhammad (saw). That is why Ali (asws) said that Allah’s curse is on those who do not say that he is the fourth of the four caliphs.

Source: Manaaqib Ameer Al-Mu’mineen, ibn Shaadhan, Hadith #59 (Link); Tafseer Al-Burhaan, Volume 1, Page 169, Hadith #14 (See Image)

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In Uyoon Al Akhbar, it has been narrated from Abu Al Hassan Muhammad Bin Ibrahim Bin Is’haq as from Abu Sa’eed Al Noosy from Ibrahim Bin Muhammad Bin Haroun from Ahmad Bin Al Fadhl Al Balkhy from Khaly Yahya Bin Sa’eed Al Balkhy
(It has been narrated) from Ali Bin Musa Al-Reza (as) from his father (as) from his forefathers (as) from Ali (as), who said: ‘While I was walking with the Prophet (sawa) in a road of Medina, we met a tall old man with a bushy beard and broad shoulders. He saluted the Prophet (sawa) and greeted him, then turned towards me (Ali (as)) and said: ‘Peace be upon you O fourth Caliph, and Mercy and Blessing of Allah be upon you!’ He then turned towards the Prophet (sawa) and said: ‘Is this not the case, O Rasool-Allah (sawa)?’ Rasool-Allah (sawa) said to him: ‘Yes it is’. The man then walked away.
I (Ali (as)) said: ‘O Rasool-Allah! What is this that this Sheykh said that you (sawa) ratified?’ He (sawa) said: ‘You are that (the fourth caliph), and Praise be to Allah (swt). Verily Allah has Said in His Book [2:30] “I am going to Make a Caliph in the earth” and so Adam was the first Caliph. And the Might and Majestic Says [38:26] “O Dawood ! Surely We have Made you a Caliph in the land; so judge between the people with the Truth;” he was the second, and the Mighty and Majestic Relates the story of Musa (as) when he said to Haroun [7:142] “Be my Caliph, and act well” It was Haroun (as) that Musa (as) appointed as Caliph in his community and he was the third. And, the Mighty and Majestic Says [9:3] And a proclamation from Allah and His Rasool to the people on the day of the greater Pilgrimage and you (as) were the Preacher (Adhan) from Allah Mighty and Majestic and from His Rasool (sawa), and you are my Trustee and my successor and the fulfiller of my debts and the my representative and your status with me is that of Haroun (as) with Musa (as) except that there will be no Prophet after me. You are the fourth Caliph as the Sheykh had greeted you. Do you know who he was?’ I said: ‘No’. He (sawa) said: ‘That was your brother Al-Khizr (as)’.

Source: Tafseer Noor Al-Thaqalain, Volume 1, Hadith #73 (See Image)

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Conclusion

Not only is there a wisdom behind this statement (a protection for the believer) but there is also insult to those who usurped his (as) rights. Imam Ali (as) is the fourth caliph of the four mentioned on the tongue of Rasool-Allah (swt), and the others are no more than illegitimate rulers not worthy of recognition of the Caliphate. May Allah (swt) raise us with Ali (as) and the Ahlulbayt (as) and may Allah (swt) strengthen your deeds on this day of the Martydom of the Messenger of Allah (swt).