It depends on what you mean by 'pixel'?
If you simply want to know the gridcell count of the grid you have created, right-click the layer in 'Table of Contents', press 'Select Attribute Table', and then look at how many objects that you are able to select in the lower fame (0 out of X selected), this is the total gridcell count.
You might have to be more specific about your problem and what you are interested in knowing. If you are interested in knowing how many pixels of a raster that is in each fishnet gridcell this might be difficult since a grid is made of polygons and a regular supervised classified image is a raster, so you would have to transform the raster to polygons, and instead look at area.
you can go in this link
http://desktop.arcgis.com/en/arcmap/10.3/manage-data/raster-and-images/using-the-pixel-inspector.htm
Please use Zonal Statistics as Table. For feature zone data, use your fishnet grid as polygon Shapefile. Set statistics type as ALL, it will give you the count of pixels in each of your fishnet grid. Hope it helps.
@ Amir Sohil Choudhury
I think @Carl Alexander Frisk has given the right suggestion…….so you would have to transform the raster to polygons.
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