This article assumes that you have downloaded and installed the Sage CRM Twitter component for Sage CRM v7.1. This can be obtained from the Marketplace.
Below is a Simple List Gadget that displays the Companies for which I have recorded the Twittername.
The Twitter component adds several fields into different tables within Sage CRM. There are 2 fields added to the company table which are comp_xttc_savedsearch and comp_xttc_username. It is the latter one that contains the Twittername when it is saved for a company. E.g.
The List Gadget is based on an Advanced Find which will search for those companies that have a value in the comp_xttc_username field.
The search clause is
WHERE (COALESCE(comp_xttc_username, '') <> '')
There are plenty of articles about List gadgets on the community. I have also written about using an Advanced Find before in the article "Using an Advanced Find as a Data source for a List Gadget"
I saved my Advanced Find as 'Twitter Contacts' and this was then available as a data source for a the List gadget.
You can find a short training video that explains how to create a List Gadget here: https://www.sagecrm.com/player/videos.htm