I have data for one small area and I want to extrapolate ( with an acceptable level of confidence) it for more larger area using kriging (the bigger area is larger twice that the small one)..this data shows a trend with the altitude.
You have a number of threads open on interpolation and extrapolation.
For example.... https://community.esri.com/message/724513-extrapolation
Why don't you go back to those threads and provide some feedback there on what worked and what didn't work.
There is little point in providing more advice since a lot of advice was given there, specifically
I think that about covers it all, so search for threads that you have 'Authored' on the left and read the advise provided first.
Please revise the comment made by Steve Lynch in your other thread on the same topic: https://community.esri.com/thread/204080-extrapolation#comment-724560
The only way to use kriging is to edit the data and create additional points that cover the entire area based on the relationship that you determined between altitude and the measurements you want to extrapolate. Although I seriously doubt that you should do that.