Answer
✅Answer: Please pay attention to the following narration:
1 جَعْفَرُ بْنُ الْحَسَنِ الْمُحَقِّقُ فِي الْمُعْتَبَرِ عَنْ جَمِيلٍ عَنْ أَبِي عَبْدِ اللَّهِ قَالَ: قُلْتُ تَفُوتُ الرَّجُلَ الْأُولَى وَ الْعَصْرُ وَ الْمَغْرِبُ وَ يَذْكُرُ بَعْدَ الْعِشَاءِ قَالَ يَبْدَأُ بِصَلَاةِ الْوَقْتِ الَّذِي هُوَ فِيهِ فَإِنَّهُ لَا يَأْمَنُ الْمَوْتَ فَيَكُونُ قَدْ تَرَكَ الْفَرِيضَةَ فِي وَقْتٍ قَدْ دَخَلَ ثُمَّ يَقْضِي مَا فَاتَهُ الْأَوَّلَ فَالْأَوَّلَ.
📚Al-Mu'tabar, p. 236
Jamil said: 'I said to Imam Sadiq (peace be upon him): 'A person misses the noon, afternoon, and sunset prayers and remembers them after the time of the evening prayer has begun. (What should such a person do?)?'
The Imam said: 'He should begin with the prayer that is in its time (i.e., he should first perform the evening prayer, which is in its time) because he is not safe from dying, and in that case, he would have abandoned an obligatory prayer whose time has arrived. Then he should perform the prayers that he missed in order.'
✅In the above narration, it is clear that a person who is busy performing past missed prayers, if the time for the current daily prayer has arrived, should first perform this prayer and then perform the missed prayer.
✅In the following narration and others like it, permission has also been given to perform the missed prayer as long as there is no fear of missing the current prayer:
2 عَنِ الْحُسَيْنِ بْنِ سَعِيدٍ عَنِ ابْنِ أَبِي عُمَيْرٍ عَنْ عُمَرَ بْنِ أُذَيْنَةَ عَنْ زُرَارَةَ عَنْ أَبِي جَعْفَرٍ فِي حَدِيثٍ قَالَ: إِذَا دَخَلَ وَقْتُ صَلَاةٍ وَ لَمْ يُتِمَّ مَا قَدْ فَاتَهُ فَلْيَقْضِ مَا لَمْ يَتَخَوَّفْ أَنْ يَذْهَبَ وَقْتُ هَذِهِ الصَّلَاةِ الَّتِي قَدْ حَضَرَتْ وَ هَذِهِ أَحَقُّ بِوَقْتِهَا فَلْيُصَلِّهَا فَإِذَا قَضَاهَا فَلْيُصَلِّ مَا فَاتَهُ مِمَّا قَدْ مَضَى.
📚Al-Kafi, Vol. 3, p. 292
Imam Baqir (peace be upon him) said in a hadith: 'When the time for a prayer arrives and he has not yet finished the missed prayers, as long as he does not fear missing the time of this prayer that has arrived, he can perform the missed prayers, but this prayer (whose time has arrived) is more deserving of its time, so he should perform this prayer (whose time has arrived), and when he has performed it, he should perform the past missed prayers.'
✅Important Note: If our missed prayer is the previous prayer, it is necessary, if there is ample time and no fear of missing the current prayer, to first perform the previous missed prayer and then perform the current prayer. You must see its narration in the following link:
اللَّهُمَّ فَصَلِّ عَلَی مُحَمَّدٍ وَ آلِ مُحَمَّدٍ وَ عَجِّلْ لِوَلِیِّکَ الْفَرَجَ وَ الْعَافِیَةَ وَ النَّصْرَ