A fellow Shia brother and I were having a conversation about the martyrdom of Bibi Fatima and wondering what are the Shia narrations for the incident of the burning door? are they in our most authentic books are did our early scholars believe the story to be authentic. would love some references I can pass along.

There are narrations from both shia and Sunni sources regarding the incident of attacking the house of bibi Fatima (as) :
Some shia sources:

1) Ibn Qawlawayh narrated in his book ‘Kamilul Ziyarat’ in a reliable hadith from Hammad Bin ‘Uthman from Imam Al-Sadiq (a.s.): On the night of the Prophet’s ascension, it was said to him (the Prophet): “Allah will test you in three things” and he started counting them… then he said “as for your daughter, she will be oppressed and deprived (of her right) and her right (to Fadak) that you will give to her will be seized from her and she will be hit while she is pregnant, and her house (and privacy of her family) will be entered without permission, then weakness and humiliation will be inflicted upon her and she will not be able to prevent it, and she will miscarry her baby from all the hits she will suffer, and she will die as a result of those hits … and the murder of Muhassan bin Ali will be the first crime that the killer (Umar) will be accountable, and then Qunfuth, so they will both attend (the judgement).” (Kamilul Ziyarat 232)

2) Yunus bin Ya’qub has narrated from Imam Al-Sadiq (a.s.) that the Imam said: O Yunus! My grandfather the Messenger of Allah said “Cursed is the one who will oppress my daughter Fatima after I die, and seize her right and kill her!” (Kanzul Fawa-id 1:149)

3) Al-Kulayni has narrated from Abi Basir from Imam Al-Sadiq (a.s.) who said: Amir Al-mumineen (i.e. Imam Ali) said: “Your miscarried babies whom you do not name before they die, will meet you on the Day of Judgement, and the baby will ask it’s father “Did you not give me a name?” Verily the Messenger of Allah (s.a.w.s.) named Muhassan before he was to be born.” (Al-Kafi 6:18)

4) Muhammad bin Harun Al-Talakbari has narrated in a reliable narration from Abi Basir from Imam Al-Sadiq (a.s.) who said: Fatima was born on the twentieth day of Jamadil-akhira, forty-five years after the birth of the Prophet. And the cause of her death was that Qunfuth, the slave of the man (i.e. Abu Bakr), by the command of his master (Abu Bakr), hit her with his sword, from which she miscarried Muhassan, and she became severely ill from this event. And she did not allow anyone of those whom harmed her to enter her house. There were two of the companions of the Prophet (i.e. Umar and Abu Bakr) who asked Amir Al-mumineen (Imam Ali) to intercede on their behalf (and ask Fatima to allow them to enter). He (Imam Ali) asked her and she permitted (for them to enter). When they entered, they remarked “How are you O daughter of the Messenger of Allah?” She replied “I am well, praise to Allah”. Then she told them both, “Have you not heard the Prophet say “Fatima is a part of me, whosoever hurts her has in fact hurt me, and whoever hurts me has in fact hurt Allah”?” They both affirmed that. She said “I swear by Allah that you have both hurt me.” So they both left the house and she was displeased with them. (Dala-il Al-Imamah 45)

5) Sayyed Bin Tawoos has narrated in his book Al-Turaf on the authority of Imam Al-Kathim (a.s.) who said: When the Messenger of Allah was in the last stages of his life, he summoned people of the Ansar and told them “Verily Fatima’s door is my door and her house is my house, whosoever violates it has in fact violated the sanctity of Allah.” The Imam cried for a while and could not continue his words, then he said: “I swear by Allah, the sanctity of Allah has been violated! I swear by Allah, the sanctity of Allah has been violated! I swear by Allah, the sanctity of Allah has been violated! O my mother, blessings of Allah upon her!” (Bihar Al-Anwar 22:476).