Shia does not believe in another version of Quran and Mushaf Fatima has nothing to do with Quran.
Aware that there is no ground for accusing the Shia of having another Quran by saying that Shia believe Fatima to be a messenger of Allah and they believe her book's name is Mushaf of Fatima.
According to Usul al-Kafi as narrates from Imam Sadiq she died 75 days after the demise of the Prophet. She was very sad because of the death of her father, so Gabriel used to come and express his condolences to Fatima and speak about the place of the Prophet in Paradise to make her rejoice. Gabriel also explained about what would happen to her children. Imam Ali (as) wrote them down in a collection later called Mushaf Fatima.(1) It was not matter of prophethood. According to Quran such inspiration has happened before to the mother of Moses and even to bees. It is clear it has nothing to do with prophethood.
when We revealed to your mother {Moses's mother} whatever was revealed (20:38)
Your Lord has revealed to the bees to select a place for living from the mountains. (16:68)
See Usul al-Kafı, no 638
Notes:
1. . مُحَمَّدُ بْنُ يَحْيى، عَنْ أَحْمَدَ بْنِ مُحَمَّدٍ، عَنِ ابْنِ مَحْبُوبٍ، عَنِ ابْنِ رِئَابٍ، عَنْ أَبِي عُبَيْدَةَ، قَالَ: سَأَلَ أَبَا عَبْدِ اللَّهِ عَلَيْهِ السَّلَامُ بَعْضُ أَصْحَابِنَا عَنِ الْجَفْرِ، فَقَالَ: «هُوَ جِلْدُ ثَوْرٍ مَمْلُوءٌ عِلْماً». قَالَ لَهُ: فَالْجَامِعَةُ؟ قَالَ: «تِلْكَ صَحِيفَةٌ طُولُهَا سَبْعُونَ ذِرَاعاً فِي عَرْضِ الْأَدِيمِ مِثْلُ فَخِذِ الْفَالِجِ، فِيهَا كُلُّ مَا يَحْتَاجُ النَّاسُ إِلَيْهِ، وَ لَيْسَ مِنْ قَضِيَّةٍ إِلَّا وَ هِيَ فِيهَا حَتّى أَرْشُ الْخَدْشِ». قَالَ: فَمُصْحَفُ فَاطِمَةَ؟ قَالَ: فَسَكَتَ طَوِيلًا، ثُمَّ قَالَ: «إِنَّكُمْ لَتَبْحَثُونَ عَمَّا تُرِيدُونَ وَ عَمَّا لَاتُرِيدُونَ، إِنَّ فَاطِمَةَ عَلَيْهَا السَّلَامُ مَكَثَتْ بَعْدَ رَسُولِ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَ آلِهِ خَمْسَةً وَ سَبْعِينَ يَوْماً، وَ كَانَ دَخَلَهَا حُزْنٌ شَدِيدٌ عَلى أَبِيهَا، وَ كَانَ جَبْرَئِيلُ عَلَيْهِ السَّلَامُ يَأْتِيهَا، فَيُحْسِنُ عَزَاءَهَا عَلى أَبِيهَا، وَ يُطَيِّبُ نَفْسَهَا، وَ يُخْبِرُهَا عَنْ أَبِيهَا وَ مَكَانِهِ، وَ يُخْبِرُهَا بِمَا يَكُونُ بَعْدَهَا فِي ذُرِّيَّتِهَا، وَ كَانَ عَلِيٌّ عَلَيْهِ السَّلَامُ يَكْتُبُ ذلِكَ، فَهذَا مُصْحَفُ فَاطِمَةَ عَلَيْهَا السَّلَام».