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i am not sure to understand your question but the following link makes a good job at introducing sufficient, complete and ancillary statistics

http://www.math.uah.edu/stat/point/Sufficient.html

"A sufficient statistic contains all available information about the parameter; an ancillary statistic contains no information about the parameter."

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Thank you Fabrice

My question is in Sufficiency statistics its conditional distribution is free from parameter

and also in ancillary statistics free from parameter.

If there are relation or difference between them?

Sorry to say i could not get any clear idea from your link.

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clearly, i have not understood your question (i do not understand what is "free from parameter") ...

let's try another reference (attached below) ; go through it up to the example of the uniform distribution (3 first pages ...) which gives an example of a sufficient statistics and of a statistics which is not sufficient

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If the conditional distribution of Sampling distribution is independent of Parameter is called sufficient statistics.

An ancillary statistic is a statistic whose sampling distribution does not depend on the parameters of the model

So what are difference between them Fabrice? I studied more than 3 or 4 days all internet material but unfortunately did get and deep knowledge.