Salam what’s the best way to go about doing my Qadha prayers.
How should I fit in my day. And should I do salah tul layl also or just stick to completing my qadha prayers first?

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The best and practical way for fulfilling your qadha is offer it after every wajib salat and only one namaz so you will not be tired e.g. after Fajr Salat pray only 2 rakat Fajr of your qadha after Zohar salam one qadha of zohr.
But if you don’t have time at Zohr (Noon) because at that time you are at work or college then manage your Zohr and Asr qadha at Fajr time.