I want to create a new text field below the post title, where the byline/ingress should be. For example:

MAN WETS HIMSELF IN PUBLIC
Police now raises bed wetting-awareness <--- This text!

Blablablabla

*footer*

So... basically I want a second title with smaller text but still high SEO (not as high as the title obviously). Is this possible? How do I do it? Any good plugins? Can I change it in atahualpa somehow?

Thanks!

There used to be some sub-heading plugins. I would try a search on wordpress.org. Alternatively you can just add the text into the post or page itself and add your h tag as applicable.