How to separate category based on invoice Date, invoice number and category

I have a table like below

I need new category like below

Note: If bill Date is same and Bill No is duplicate and category is different then consider VSS.

I tried

SELECT Date, BillNo, Category 
    , case when [Category]='VSS' then 'VSS' else 'RSS' end [New CATEGORY] 
FROM TBL

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