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: