How authentic is the Hadith: "May Allah have mercy on a person who prays four rak'ahs before Asr," and is praying four rak'ahs after the Adhan of Asr and before the Asr prayer valid, or is what is meant that this prayer should be between Dhuhr and Asr?

The hadith in question was narrated by Ahmad, Abu Dawud, and Al-Tirmidhi from Ibn Umar that the Prophet (peace and blessings be upon him) said: "May Allah have mercy on a person who prays four rak'ahs before Asr." The method of performing this supererogatory prayer between the adhan and the iqamah is correct.