The so claimed un-authentic hadiths, how did they come about?
Similar to Paul/Saul after the going away of Jesus, people will use his name for their purposes. Ditto for Prophet Muhammad. They will make up stories and attribute sayings to the Prophet, even when he said no such thing. They want to ride on the Prophets authority.
That's how most religions morph and change into something totally unlike what was taught eg, Christianity.
If they can corrupt the bible, they can lie about prophets.
Fortunately Muslims have a systematic way of sussing out the fake hadiths and it's criteria so stringent that if it was applied to the bible, it would immediately fail even before one opens it.
Factors like did they actually met and crossed paths?
Who else reported the same?
Who wrote down the Hadith?
Who are the chains of narrators?When did the event happen?
Which period did they live?
Where and when did they live?
Their biographies. Their lineage.
Does it contradict the Quran? Have they ever been caught lying? And more.
Remember the chains of narrations were passed down the generations, and the above are also cross checked down the generations too.
We even have hadiths about the same event narrated by two different persons or more, down different chains through the generations and then miraculously they reported the exact same words the prophet spoke, word for word.