We are using EN 24 Steel for axle shaft.
We are doing shot peening on these axle shafts.
Specified Arc intensity is 015 " to 0.020 " ( Almen strip A scale)
But actual measured Arc intensity is 0.060 ".

What will be the effect of this overpeening?

There are so many variables involved it is hard to predict what might happen. First, the .060 arc height on the "A" strip is excessive. You should use the "C" strip for any value over .024" arc height. I assume your part is not thin, else severe distortion would be noticed. Really, the only way to tell the effect of this peeing treatment is to perform fatigue testing. You should prepare some sample axles with the proper peening range of .015-.020" intensity and then some with the higher intensity.
I'm curious. Why is the actual intensity allowed to be so high?

sounds to me like this guy was unsing an "N" strip, thought he had an "A" strip

Your measured intensity seems to be excessive. Details of shot size and type, air pressure etc. would help towards giving advice.