linux4me2

This widget allows you to insert arbitrary Text and/or HTML code (optional) to precede a list of recent posts by category. It makes it easy to add introductory comments and to achieve interesting effects like wrapping your posts list around an image. It’s designed to be lightweight and easy on resources.
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Note: Widget Blocks, added in WordPress 5.8, make this plugin no longer necessary. The same results can be obtained by using a Widget Group, Heading Block, Custom HTML Block, and the Latest Posts Block. The latter also allows the use of multiple categories, which is not available with this plugin. Unless something major happens to change things, I won’t be developing the plugin beyond the current version (2.0.0).
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HTML Plus Recent Posts by Category Widget

Like the Legacy Recent Posts widget, but adds the ability to select the category and add text or HTML before the list of posts.

Prasanna SP

This plugin creates a new widget which lets you show a list of recent posts based on categories or tags. This is a must have plugin if you want to exclude some categories in recent posts widget or if you want to show recent posts based on tags. By default the wordpress recent posts widget shows a posts from all category. But this plugin gives you more power to customize your recent posts widget. You can also display post date in the widget.
See the live action of this plugin on <a href="http://demo.prasannasp.net/custom-recent-posts-widget/" rel="nofollow ugc">demo site</a> or on Kennneth John Odle’s <a href="http://blog.kjodle.net/" rel="nofollow ugc">blog</a>.
Have any questions or suggestions? Create a thread in the <a href="http://forum.prasannasp.net/forum/plugin-support/custom-recent-posts-widget/" rel="nofollow ugc">support forum</a>.
Visit <a href="http://www.prasannasp.net/wordpress-plugins/" rel="nofollow ugc">this page</a> for more WordPress Plugins from the developer.
A special thanks to <a href="http://blog.kjodle.net/" rel="nofollow ugc">Ken</a> and <a href="http://www.joshlobe.com" rel="nofollow ugc">Josh</a> for testing the code.

Custom Recent Posts Widget

A widget to show recent posts list based on categories or tags

HTML Plus Recent Posts by Category Widget vs Custom Recent Posts Widget