when you said on a period time and during a period time ,what is the difference ?
So sorry I may make a misunderstanding,the a period of time thing just an metaphor,what I really mean is like on a vacation and during the vacation ,on the lunch and during the lunch .I can make a sentences ,like just one guest didn't perform well on the wedding or just one guest didn't perform well during the wedding.

Question

when you said on a period time and during a period time ,what is the difference ?
So sorry I may make a misunderstanding,the a period of time thing just an metaphor,what I really mean is like on a vacation and during the vacation ,on the lunch and during the lunch .I can make a sentences ,like just one guest didn't perform well on the wedding or just one guest didn't perform well during the wedding.

Answer

In American English you can say"period of time" or "time period", but not "period time".  X happened during that time period.

Answer

"on a period of time" is incorrect.

Answer

You have to say "period of time" in every case.
You don't use "on a period of time" in any context.
"Something happened during a specific period of time" means that the thing happened in the period but not necessarily over the whole period.  
"Something happened over a period of time" means that the thing happened throughout the whole period.