If you show your code, I will try to assist you in what you are working on, but only one step at a time. So I only need to know what your current programming question is and how I can exactly help you. I am replying to your request for help because you seem adept enough to handle this. If you need someone to do this for you please submit your inquiry to the unpaid/paid request forums.
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I tried in the first step to add condition to the widget template (I just use the default php eval widget to understand things), but I didn't figure out what is the condition that I must use in template to say this page is section or article !!
Show me the code and your condition for this widget... and carefully explain what you want (just) this conditional to do.
Have you successfully cloned a widget by using a new template? This is where you would add the additional template conditionals and variables you require -- of course they would have to be available from the PHP code.