We post content three times a week on a powerful site related to our site and link in all content with a fixed phrase to the home page of our site. Will SEO be beneficial or harmful?
Let's see? You give content away. You link to your home page with short keyword centric links. All this from the same site. Hummm. Not good.
Stop giving content away. And stop making keyword loaded links to your home page or anywhere else. The links alone can get your site penalized if done enough. Create content for your site and encourage organic links instead of artificially created keyword loaded links. Especially from a single site.
People use social media for organic linking these days. Engaging users and promoting content via social media is paramount these days.
Inbound links should be high quality, organic, and diverse in origin meaning from many sites where site owners created the site without your input. There are no shortcuts in creating search performance. None.
As a side, there is a ton of extremely poor SEO information out there. Take 99% of it and chuck it out the window! Read as much as you can and in short order you will see more clearly on the subject. I promise!