Al-Dārimī (1/26) and al-Daylamī (1/2/308) recorded it.

This chain is acceptable as supporting evidence, for Zamʿah is weak, though Muslim cited him alongside another narrator; and Salamah—i.e., Ibn Wahrām—is likewise weak, or perhaps in a somewhat better condition than he is. Al-Tirmidhī may well have deemed it good because of this supporting narration. And Allah knows best.

Note: Al-Suyūṭī attributed the hadith under this heading to al-Tirmidhī and Aḥmad, but I have not found it in al-Musnad with this wording. Rather, Aḥmad recorded it there (3/144 and 247–248) through two other routes, and al-Dārimī (1/27–28) recorded it through one of them, from Anas, within his lengthy hadith on intercession. It states: “Then I shall come to the gate of Paradise, take hold of the ring of the gate, and ask for it to be opened….”

Muslim (1/130) also recorded it through another route from Anas, in abbreviated form: “I shall have the greatest following of all the Prophets on the Day of Resurrection, and I shall be the first to knock at the gate of Paradise.” Abū ʿAwānah likewise recorded it in his Ṣaḥīḥ (1/109). In a version recorded by both of them: “I shall be the first of mankind to intercede concerning Paradise, and I shall have the greatest following of all the Prophets.” Al-Khaṭīb also recorded it in al-Fawāʾid, no. 12 in my copy. In another version recorded by both of them: “I shall be the first intercessor in Paradise. No Prophet has been believed as I have been believed; indeed, among the Prophets is one whose entire community includes only a single man who believed in him.” Abū ʿAwānah’s wording is: “…among the Prophets is one who will come before Allah on the Day of Resurrection with only one man who believed in him.”

Abū Nuʿaym also recorded another route for it in Ṣifat al-Jannah (folio 30/2), through the narration of Ziyād al-Numayrī from Anas, directly attributed to the Prophet, with the wording: “I am the first to take hold of the ring of the gate of Paradise, and this is no boast.” Ziyād is weak.