I am working on multiple shapefiles at once and I want to shift the shapefiles in a particular direction by 15m at the same time keeping the original shapefile on place. Kindly guide me for the same.
description of my task to be done

I have tried through buffering, but its is not giving the desired results.
I guess, it could be solved using a custom projection. I'm not sure if you use ArcGIS Pro or ArcMap. This description works for ArcMap:
If this works for you, you could try to automate it via the model builder. (I use a german version of ArcMap, the propper english naming could differ a little bit)
Example for germany, using 1500 m shift
Another option would be to use FME Workbench. It includes the offsetter and is afaik free to try for 30 days. Also it is very usefull for batch transformations.
Additional idea: solve it, using arcpy like this: