Sayyidah Maymunah (may Allah be pleased with her) said: The Prophet (peace and blessings be upon him) used to pray two rak'ahs before Asr.
Abu Ya'la and al-Tabarani in al-Mu'jam al-Kabir and al-Mu'jam al-Awsat recorded it; its chain contains Hanzalah al-Sadusi, whom Ahmad and Yahya bin Ma'in declared da'if (weak), while Ibn Hibban declared him thiqah (trustworthy).
Sayyidah Umm Habibah bint Abi Sufyan (may Allah be pleased with her) said: The Prophet (peace and blessings be upon him) said: "Whoever regularly prays four rak'ahs before Asr, Allah Almighty will build a house for him in Paradise."
Abu Ya'la recorded it; its chain contains Muhammad bin Sa'd al-Mu'adhdhin, and I do not know him.
Sayyidah Umm Salamah (may Allah be pleased with her) narrates that the Prophet (peace and blessings be upon him) said: "Whoever prays four rak'ahs before Asr, Allah Almighty makes his body forbidden to Hellfire." I said: "O Messenger of Allah! I have seen you sometimes pray these rak'ahs and sometimes leave them." The Prophet (peace and blessings be upon him) said: "I am not like any one of you."
Al-Tabarani recorded it in al-Mu'jam al-Kabir; its chain contains Nafi' bin Mihran, and there are other narrators besides him whom I did not find anyone mentioning.
Sayyiduna Abdullah bin Amr bin al-As (may Allah be pleased with him) said: I came while the Prophet (peace and blessings be upon him) was among some of his Companions, among whom was Sayyiduna Umar bin al-Khattab (may Allah be pleased with him). I caught the last part of his (peace and blessings be upon him) talk; the Prophet (peace and blessings be upon him) was saying: "Whoever prays four rak'ahs before Asr, the Fire will not touch him."
Al-Tabarani recorded it in al-Mu'jam al-Awsat; its chain contains Abd al-Karim Abu Umayyah, who is da'if (weak).
In al-Mu'jam al-Kabir it is transmitted in abridged form with these words: "Allah Almighty will make him forbidden to Hellfire."
Sayyiduna Ali bin Abi Talib (may Allah be pleased with him) narrates that the Prophet (peace and blessings be upon him) said: "The people of my Ummah will continue to pray these four rak'ahs before Asr until they walk upon the earth in a state where they have definitely been forgiven."
Al-Tabarani recorded it in al-Mu'jam al-Awsat; its chain contains Abd al-Malik bin Harun bin Antarah, who is matruk (abandoned).