Expedition of Ali ibn Abi Talib, to convert the people of Yemen to Islam, took place in 10AH or 631 AD.
Military Expedition
According to Ar-Rahīq al-Makhtum (the Sealed Nectar), a modern Islamic hagiography of Muhammad written by the Indian Muslim author Saif ur-Rahman Mubarakpuri, Khalid ibn al-Walid was appointed with the people of Hamdan to call them to Islam. He stayed with them for 6 months but they did not convert. Then Muhammad dispatched Ali ibn Abi Talib and Khalid came back to Muhammad. Ali called them to embrace Islam (and communicated a message from Muhammad to them), and they responded and embraced Islam. Ali then wrote to Muhammad about his success, to which Muhammad replied "Peace be upon Hamdan, Peace be upon Hamdan". Khalid ibn al-Walid was not able to convert the people of Hamdan in 6 months, but Ali reportedly managed to convert all the people of Hamdan in 1 day.
Islamic Primary sources
The event is mentioned by the Muslim jurist Tabari, he wrote:
The person who narrated this event was al-Bara b. Azib, who was an ardent supporter of Ali ibn Abi Talib.