Regarding Branding the Hand of the Thief

Hazrat Ibn Thawban narrates that the Noble Prophet (peace and blessings be upon him) cut off a man's hand and then cauterized it to stop the bleeding.

The aforementioned action of the Prophet Muhammad (peace and blessings be upon him) is also narrated from this chain by Hazrat Muhammad bin Abdur Rahman.

Hazrat Amr bin Abu Sufyan narrates that a thief was brought to Hazrat Ibn Zubair, so he cut off his hand. Upon this, Hazrat Aban bin Uthman said to him: Cauterize (seal) it. He replied: You are very merciful to him. He said: No, but this act is Sunnah.

Hazrat Amr narrates that Hasan Basri said: Branding the thief is the Sunnah method.

Hazrat Hujayyah narrates that Hazrat Ali (may Allah be pleased with him) used to cut off the hands of thieves and cauterize them, then imprison them and have their wounds treated. When the wound would heal, he would say, "Raise your hands," so they would raise them as if they were red male organs. Then he would say, "Who cut your hands?" They would reply, "Ali (may Allah be pleased with him) did." He would ask, "Why were they cut?" They would reply, "We committed theft." Then he would say, "O Allah, bear witness! O Allah, bear witness! You may go."