The question is not clear.

First of all, it is not permissible to pray Isha prayer at 01:00 as this is way passed its time. Isha must be prayed before midnight which is half the time between Maghrib and Fajr.

Secondly, are you asking about witr or Istikhara? Istikhara has nothing to do with fajr or with Isha.

Finally, if you are asking about tahajjud, this has to be preceded by sleeping.

I have learned that WITR prayer should preferably be prayed as the last prayer of the day. But if we pray Isha late, like 1:00 AM and fajr is due at 4:35am…and we are awake through the night, then at what time is it appropriate to do ISTIKHARA?

Prayer | March 25, 2014 4:21 pm
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I had some guest in my house an it was time for isha pray and I did not want to delay the pray but I did because it was the 1st time they had visited me in quite sometime, and by the time they had went I wasn’t to sure on weather or not to pray ou were wrong in what you had done and you have committed a major sin. Were you shy from telling the people that you are a practicing Muslim and that you wanted to pray on time? Were you afraid of them more than Allah?
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There is a hadeeth of RasoolAllah s.w.a that he said the best time to pray isha is nisful layl? So I do not end up going to congregation for Isha. I stay at home expecting to pray at the best time.