As you mentioned you can either create a separate Automation that would run only on Saturdays or if it is crucial to run everything within one Automation with that specific schedule then you can do that:
1. Create Data Extension, let's call it "**Sunday_Check**" with the field "**isSunday**" (Boolean, nullable);
2. In your Automation that would have a **daily** running schedule set as a first step `Script Activity`:
```
<script type="javascript" runat="server">
Platform.Load("Core", "1");    

/* Cleans whole Data Extension */
var prox = new Script.Util.WSProxy();
var action = "ClearData";
var props = { CustomerKey: 'xxxx' }; /* Change 'xxxx' to Data Extensions' External Key */
var data = prox.performItem("DataExtension", props, action);

/* Checks if today is Sunday, then add record to DE */
var isSunday = (new Date().getDay());
if( isSunday == 0 ) /* Sunday = 0, Monday = 1 and so on */
    var rowAdd = Platform.Function.InsertData('Sunday_Check',['isSunday'],['True']);
else 
    
</script>
```
3. In the Automation add `Verification Activity` to validate "Sunday_Check" Data Extension having `Count is greater than 0` then stop the automation
4. This way, each day you would have a check whether today is Sunday and if it is then the DE would be populated with a record, and the Verification Activity would stop the Automation because of that. On other days, it would simply let the Automation run the next steps.