Saying Allahumma ajirni min an-nar 7 Times
Question

Has it been authentically narrated that one should say 'Allahumma ajirni min an-nar', seven times after Fajr (early morning) and 'Isha prayers?
Praise be to Allah.Hadith about saying “Allahumma ajirni mi nan-nar” 
This hadith (prophetic narration) was narrated by al-Imam Ahmad in al-Musnad, 17362, and by Abu Dawud, 5079. The hadith is as follows: 
Prophet Muhammad (peace and blessings of Allah be upon him) said: “When you pray Fajr, then say before speaking to any of the people, ‘Allahumma ajirni min an-nar (O Allah, protect me from the Fire)’ seven times. Then if you die on that day, Allah will grant you protection from the Fire. And when you pray Maghrib, then say before speaking to any of the people, ‘Allahumma inni as-aluka al-jannah, Allahumma ajirni min an-nar (O Allah, I ask You for Paradise, O Allah, protect me from the Fire)’ seven times. Then if you die that night, Allah will grant you protection from the Fire.” 
Authenticity of the hadith on saying “Allahumma ajirni min an-nar”
Two things may be noted about the hadith. 
1. It does not say that this du’a (supplication) is to be said after ‘Isha (night prayer), as mentioned in the question.
2. The hadith is not sahih (authentic) in its narration from the Prophet (peace and blessings of Allah be upon him). See al-Silsilah al-Da’ifah by al-Shaykh al-Albani (may Allah have mercy on him), 1624. 
Based on this, it is not mustahabb (desirable) to recite this du’a after Fajr and Maghrib prayers. 
3. Anas (may Allah be pleased with him) said: The Prophet (peace and blessings of Allah be upon him) said: “Whoever asks Allah for Paradise three times, Paradise will say, ‘O Allah, admit him to Paradise.’ Whoever seeks protection from the Fire three times, Hell will say, ‘O Allah, protect him from the Fire.’” (Narrated by al-Tirmidhi, 2572; Ibn Majah, 4340. This is a sahih hadith; it was classed as sahih by al-Shaykh al-Albani (may Allah have mercy on him) in Sahih al-Jami’, 6275) 
But there is nothing to state that this should be recited in conjunction with any particular prayer, or at any particular time. 
It is mustahabb for the believer to ask Allah for Paradise a great deal, and to seek protection from Hell a great deal, without saying such words in conjunction with any particular prayer, or at any particular time.
For more, please see these answers: 217496 , 105396 , and 148174 .
And Allah knows best.