This indeed is a sad issue that seems to never be solved. The earliest of Shi'ah scholars have addressed this in detail, establishing the completeness and perfection of the Quran, being the everlasting miracle of Islam.
Books have been written, detailed extensive research has been made, and statements so ever frequently given, all explaining the position of Shi'ah Muslims regarding the holy Quran.
However, with such abundant sources openly available for all to read, we see that some Sunnis persist on accepting this myth and want nothing to do with any of the solid evidence presented against it.
The cliche referencing of Kitab Ali (a.s.) is brought up, or Mashaf Fatimah (a.s.), even though it has nothing to do with the holy Quran.
If only someone could dig up this 'different Quran' Shi'ahs supposedly believe in.
Do these accusations come from ignorance, or is it just malice intent fueled with hatred.
1. Twelver Shi'ahs believe the very Quran that is with us all today is the only and only Quran all Muslims believe in and accept.
2. This Quran is complete, and perfect, in every form and way, with no surah or verse missing, and there is no extra surah or verse added to it.
3. If, for argument sake, there is a Shi'ah scholar who has a view that the Quran is incomplete, or any other view of this sort, it is their view, and it does not represent the belief of the Shi'ah Creed. It is far from genuine and fair to use the singular views of one or two scholars and generalise it to be the foundational belief of the whole Shi'ah creed.
4. If there are narrations that elude to certain surahs/verses added, or taken away, then they are rejected and not accepted.
5. There are numerous examples of this that exists in Sunni sources, like the goat eating parts of a Quran that was forever lost. However, Shi'ah Muslims have never used this to accuse Sunni Muslims of such baseless accusations.
It is very important to be truthful to ourselves and avoid biased or baseless information.
This is a contemporary book that discusses this topic in detail: