Timing for Tahajjud start right after Isha until Fajr. You may pray at anytime during that duration. But the best time is last third of the night which may be between 1.00AM to 03.20 which is half an hour before Fajr. Allah knows best
What i found is easiest is checking the time from isha to fajr and splitting it into 3🤣it seems silly but its helped me x
Timing for Tahajjud start right after Isha until Fajr. You may pray at anytime during that duration. But the best time is last third of the night which may be between 1.00AM to 03.20 which is half an hour before Fajr. Allah knows best