How to add a text widget on the posts admin page?

You can add a “Meta Box” to the admin screen of edit post/page. WordPress have the function add_meta_box function for this job. The content inside this meta box is your choice. You can define, on which area of the edit screen will add the box, like sidebar or central area. Also you have the benefits, that it would create with the default WP admin style and the option for each user to deactivate or close the box.

You find a documentation in the codex: http://codex.wordpress.org/Function_Reference/add_meta_box

Tutorials, hint and examples can you find here on WPSE or via Search on www.

A example in a screenshot, much easier to view the result.
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