I created an armature through skin modifier but it's invisible!

Does anyone have an idea why I can’t see the armature in object or edit mode? When I
click armatures name , only the white circle is highlighted.

As selected in your outliner window, your Armature is in your scene, inside of your character. Switch to wireframe and you ll see it selected.
Be sure that you didn’t hide Armature There:

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Also…set visibility to In-Front…