Hello every i am new to wordpress. I want to make my own widget which have a category selection option on backed and able to display posts from selected category on front.
I'd start with a basic widget tutorial.
From there, I'd add a dropdown on the widget back end that lists out all the categories, so you can select from existing categories.
Then on the widget front end, I'd do a WP_Query to pull a specific number of posts from that category. With posts selected, do a foreach loop to display the
<li> with link and title. Depending on your scenario, you might also want to allow the admin to choose that limited number in the widget back end, or you might just want to hard-code it to show, say, 7 posts at maximum.
Give it a try and then if you're having specific issues post your code as an edit to the original question for a bit more guidance.