I know there are applications like iAwards and Trophies and Medals, but I need something simpler.
My idea is to give an award or badge in postbit to users who care about writing correctly in the forum.
Can you think of a way to do it?

Yes.

I have a “verified badge”, which I manually apply to users. There is a custom profile field, which only the admin can change. The field has two options which then output one of two images. One is an invisible 1x1 image, the other is the actual badge. 

You should be able to adopt this for your needs. 

Thank you @opentype,

In my case I don't need, but I can view the option "Show on registration page?"

9 hours ago, opentype said:

Yes.

I have a “verified badge”, which I manually apply to users. There is a custom profile field, which only the admin can change. The field has two options which then output one of two images. One is an invisible 1x1 image, the other is the actual badge. 

You should be able to adopt this for your needs. 

Thank you @opentype It works correctly and is just what I needed.

A couple of questions:
- How to make it to be seen in the mobile version?
- How to make it appear in the user's profile?