I have different data sets (point shapefile) and how can I get common point points of these shapefile in ArcGIS?
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Assuming you just want to select them in the layer, the easiest way is to do it by using the "Select by location" tool. Choose both layers and select the "are identical" relationship. That way you will get a selection that includes all points that are identical in both layers.
Additionally, if you want to get a layer that includes those points, after selecting them just right click on the layer, Data > Export Data > Only selected features.