What should a man do who intended to pray Asr, but joined the Dhuhr prayer behind the Imam, then remembered his error in intention after the first rak'ah?

If a worshipper, while performing the Dhuhr prayer, is led by an Imam but intends to pray Asr, and either mistakenly intends Dhuhr or has no specific intention, then the Asr prayer is invalid because intention is a prerequisite for the validity of prayer. The intention must be present at the time of the takbirat al-ihram (the opening takbir) or shortly before it. If someone realizes an error in their intention during the prayer, they must interrupt the prayer and restart it. However, if what occurred was merely a waswasa (whispering from Satan) that you are praying Dhuhr after you had correctly intended Asr in its proper place, then your prayer is valid, as it is not a condition to maintain the presence of the intention throughout the entire prayer.