Semantic Zotero integrates Zotero with Semantic Scholar to fetch and display references related to a selected paper. You can then add them to your library directly from Zotero along with the full-text PDF. For now, the visuals are pretty barebones, I will update when I have time.
To fetch references for a given paper, right click on it, select "Semantic Zotero" and then "Show references"
In the Zotero Menu bar, choosing Tools -> Semantic Zotero Options allows you to configure options such as custom Semantic Scholar API key