Is there any authentic hadith or narration regarding a Companion who forgot an appointment with the Messenger of Allah, peace and blessings be upon him, in Yathrib, and the Messenger waited for him from Dhuhr until Maghrib?

We do not know of any authentic Sunnah (definition) narration stating that a man promised the Prophet (peace and blessings be upon him) a meeting, then forgot his appointment, and the Prophet (peace and blessings be upon him) waited for him from noon (Dhuhr) until sunset (Maghrib). This has no basis.

What is known in this regard is what Abdullah ibn Abi Al-Hamsa narrated, saying: "I made a transaction with the Prophet (peace and blessings be upon him) before he was sent as a Prophet, and there remained a portion (to be paid). I promised him that I would bring it to him at his place. Then I forgot. Then I remembered after three days. I came, and behold, he was in his place. He said: 'O young man, you have caused me hardship! I have been here for three days waiting for you.'" However, this hadith (definition) is weak because one of its narrators is unknown.

What refutes the aforementioned story is that the Prophet (peace and blessings be upon him) was known for his truthfulness in keeping promises and not breaking them, as were his Companions. It is highly unlikely that any of them would forget their appointment with the Prophet (peace and blessings be upon him).

The mentioned story is more akin to the fabrications of storytellers and preachers. Therefore, one should be mindful of this and be cautious about propagating it.