assalamu alaykum, Hanafi scholars say that it is permissible to pray Fajr Sunnah prayer even if Iqamah is called and if there is a chance to catup the Fajr Fard salah after praying Sunnah. The below are the evidence they give. Abdullah ibn Abi Moosa narrates: Ibn Masood(ra) came and the Imam was in the Fajr prayer. He performed the sunnah prayer behind a pillar and then joint the Imam. (I’la al-sunan 7/101) Abdullah ibn Abi Masood (ra) narates from his father:When Sa’eed ibn al-As called them he also called Abu Moosa, Hudhayfa, and Abudullah ibn Masood (ra) before the Fajr prayers. When they left from him the salah already begun. Abdullah ibn Masood performed two rak’ahs behind a pillar and then joined the Imam. (Sharh Ma’ani al-Athar 1/255) Abu Mijlaz (ra) narrates: I entered the masjid for Fajr salah with Ibn Umar and Ibn Abbas (ra)ا. Ibn Umar (ra) entered the saff and joined the congregation whilst Ibn Abbas (ra) first performed two rak’ahs and then joined the prayer. After salah Ibn Umar (ra) sat in his place until sunrise and thereafter he performed two rak’ahs. (Sharh Ma’ani al-Athar 1/255) Muhammad ibn Ka’b narrates: Ibn Umar (ra) left home and the Fajr prayer had already begun. He prayed two rak’ahs of salah on his way before entering the masjid. (I’la al-sunan 7/105) (Sharh Ma’ani al-Athar 1/256) Ubaydullah narrates:When Abu Darda (ra) used to enter the masjid and Fajr salah had begun, he used to perform two rak’ahs in the corner of the masjid and then join the congregation. (I’la al-sunan 7/106) (Sharh Ma’ani al-Athar 1/256) When we used to find Umar (ra) started the Fajr and we had not as yet performed our salah, we used to perform two rak’ahs in the back of the masjid and then join the salah. (I’la al-sunan 7/107) (Sharh Ma’ani al-Athar 1/256) Sha’bi (ra) narrates: When Masrooq used to find the prayer already commenced, he used to perform two wo rak’ahs in the corner of the masjid and then join the rayer. (I’la al-sunan) Are above reliable?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

Abu Hurayrah narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said: “When the Iqaamah for prayer is said, there is no prayer except the prescribed prayer.” [Muslim and others]

Hanafi scholars view that it is reprehensible to perform Sunnah (supererogatory) prayers when the Iqaamah is being said, except for the two Sunnah Rak‘ahs of Fajr, as long as there is no fear of missing the congregational prayer. The two Sunnah Rak‘ahs of Fajr are excluded from the general ruling because they are the most emphatic of all of the Sunnah prayers and based on the accounts of some Companions in this regard (which are mentioned in your question). Another basis for this ruling is that Abu Haneefah and Abu Yoosuf do not view that those two Rak'ahs can be made up after finishing Fajr prayer nor after sunrise because it is a basic principle, according to them, that Sunnah cannot be made up; as it is only the obligatory prayers that are to be made up. On the contrary, Muhammad ibn Al-Hasan Ash-Shaybaani, one of the closest disciples of Abu Haneefah, said that the two Sunnah Rak‘ahs of Fajr can be made up as stated in Al-‘Inaayah by Hanafi scholar Al-Baabarti.

The majority of scholars view that the Sunnah prayer of Fajr is not to be offered after Iqaamah based on the Hadeeth named above; however, they can be made up. So, if someone misses it, he can make it up after Fajr prayer or after the sunrise to be on the safe side. For more benefit, kindly refer to Fataawa 92672, 85262, and 92389.

Allaah Knows best.