Abdullah bin Umar (may Allah be pleased with him) pledged allegiance to Ali (may Allah be pleased with him) on condition that he would not fight

It is narrated from Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) that he said: "I do not grieve over missing anything of this world as much as I regret that I did not fight the rebel group (alongside Sayyiduna Ali (may Allah be pleased with him))."

It is narrated from Ghassan bin Abd al-Hamid that the people had no doubt that Sayyiduna Ibn Umar (may Allah be pleased with them both) would give allegiance to Sayyiduna Ali (may Allah be pleased with him) on the condition that he would not take part in fighting alongside him, and Sayyiduna Ali (may Allah be pleased with him) was content with this from him.

Abu al-Hasan al-Mada'ini narrates from Musa bin Talhah bin Ubaydullah that he said: "May Allah Almighty have mercy on Abu Abd al-Rahman Abdullah bin Umar. I think that he remained upon the covenant which he made with the Messenger of Allah (peace and blessings be upon him) and did not change in it in the slightest. By Allah, Quraysh could not provoke him in their first tribulation (political conflict)." (The narrator says:) I said: This detracts from the standing of his father (Sayyiduna Umar (may Allah be pleased with him)) (because it gives the impression that Ibn Umar turned out better than his father).

It is narrated from Sayyiduna al-Bara' (may Allah be pleased with him) that he said: Ibn Umar (may Allah be pleased with them both) and I were presented before the Messenger of Allah (peace and blessings be upon him) (for participation) on the day of Badr, and he (peace and blessings be upon him) sent us back because we were too young; then we took part in the Battle of Uhud.
Imam al-Hakim says: At the beginning of this chapter I cited, from the narration of Yazid bin Harun, the statement of Sayyiduna Anas (may Allah be pleased with him) that Ibn Umar (may Allah be pleased with them both) took part in Badr, but this chain is stronger than that. Moreover, the two Shaykhs agreed on the hadith that Sayyiduna Ibn Umar (may Allah be pleased with them both) was presented at the age of fourteen and he (peace and blessings be upon him) did not permit him, and at the Trench he granted him permission, and that was the first battle in which he took part. And Allah knows best.

It is narrated from Imam Malik bin Anas (may Allah have mercy on him) that he said: Ibn Shihab al-Zuhri said to me: "Never deviate from the opinion of Ibn Umar (may Allah be pleased with them both), for he lived for sixty years after the Messenger of Allah (peace and blessings be upon him), and nothing of the sayings of the Messenger of Allah (peace and blessings be upon him) or of the affairs of his Companions remained hidden from him."