I heard that athletes that train for their sport early in the mourning have some kind of mental advantage over the ones that don't is this true?
No, not necessarily. Why do you ask? (Also, I assume you mean 'morning').
A mental advantage for time to workout is differnet with each person. Like I enjoy to workout 12pm-2pm in my garage so i can feel the hot FL heat. Everyones different!
This can be true if the event they are training for takes place early in the morning and their opponents sleep in and miss the event. When this happens, you have a distinct mental advantage over your sleeping opponent. Until they wake up, anyway. At that point, you'll lose your mental advantage.
If your sport starts at ten in the morning, and you usually work out at six at night, then yes training in the morning would give you an advantage.
placebo effect, in wich case it could benefit you mentaly.