You can say' turn over a new leaf' or 'turn a new leaf'. The second version is just a shorter way of saying the first but I've seen both used to mean take action to change one's life for the better or change one's behaviour and stop doing bad things.

The correct phrase is "turn over a new leaf". I don't know the other one.

I guess they mean the same thing, but it is better to use "turn over a new leaf" so that everyone knows what you mean.