What is the ruling on the Dhuhr prayer if the ‘Asr Adhan is called and one has not completed the first raka‘ah of it, and must it be repeated if I prayed it believing it was performed on time, then it became clear that its time had elapsed?

It is not permissible to delay the prayer beyond its prescribed time except for a valid excuse. Whoever delays it without an excuse has committed a grave sin and must repent. As for one who delays it due to an excuse, such as sleep or forgetfulness, their prayer is valid whenever the excuse is removed, and that then becomes its time. The majority of jurists do not stipulate specifying performance (ada') or make-up (qada') in the intention for prayer.