I would not call myself and expert, but I can tell what is correct and will try to explain why.
お渡しください
This is probably the most common version, which you will hear often.
This is just a more polite version of “渡してください”.
It comes from the fact that in very polite contexts you use the てform without the て(very dumped down explanation but I think in this case thats enough). お is just a polite prefix (but お can not always just be put in front if everything, because there do are rules that define it’s usage).
お渡ししてください
Grammar-wise this is also correct, but I believe that you normally won’t hear this version. Another thing is that you normally use お(verb in it’s stem form)します and お(verb in it’s stem form)いたします on yourself and not on others.
You have probably heard something like お邪魔します(おじゃまします) and similar phrases before.
For others you use お(verb in it’s stem form)になる.
お渡してください
This is, in my opinion, incorrect, because you can not put an お infront of a word and keep the rest normal.
Generally there will always be a lot of ways to say the same thing in japanese. There is always a polite and a less polite way to say something.
Here are some more examples:
お渡し願います
お渡しになってください
I hope this helped and my english is understandable.
(I am not at all a japanese expert)