I want to know the prime salat time range for each prayer. Let’s say fajar Prayer starts at 5.54 am. Then till what time you get the max prayer blessings and it is counted as prayer’s fazeelat time. For example Like till 6.15 am. And I request you to advise me regarding the fazeelat time for each prayer.

The following is from the risalat of Sayed Muhammad Taqi Modaressi

The time for the fajr prayer begins with daybreak and lasts until sunrise.
It is highly recommended to hasten to pray fajr at the beginning of its time rather than delaying it until almost sunrise, except for one who is sleeping, who forgets or who is pre-occupied. But it is best to offer this prayer before the sky becomes entirely illuminated, while it is still dark and gloomy.

Sunan pertaining to the time for prayer
It is highly recommended to hasten to prayer and offer one’s prayers at the earliest moment possible, in the preferred time (waqt al-fad?i¯la), and to avoid delaying them unnecessarily. It is also recommended to pray as soon as possible, even after the preferred time has lapsed, as the closer a prayer is offered to the beginning of its time, the better that prayer is.