But if you create a "Site Page" or "link" from Site Pages library, they wont show up on news webpart.
So, we have do the following step to post our Site Page as a news webpart.
Go to the Page created using the "Site Page" option from Site Pages library and click on "Promote"
It will give the below options. Click on "Post as News on this Site". Now your Site Page will show up on News Webpart.
Also "Save as page template" will give option to save your page as a template and it can be used for to create pages in the future