Enter your URL in Site Explorer and go to the Organic Keywords 2.0 report.
Then click on any SERP button to open the SERP table for that keyword.
From here, use the date picker to browse historical SERPs. Note that historical data is limited according to your Ahrefs plan (Site Explorer > Historical data).
You can use the "Target only" toggle to zoom in on your ranking URL for that given keyword.
Also, if you have multiple URLs ranking for the same keyword, you can see that in the URL column.
If there's more than one ranking URL, you’ll see an "X more" link. Click on it to see the SERP showing only target positions.