T-SQL insert with output expression insert Table1
OUTPUT inserted.ID, s.[Id] 
INTO @Inserted
select 
s.[Field1],
s.[Field2],
from 
@TableVariable s


why is s.[Id]  marked by red line ? Is it non-correct syntax to save value in @Inserted table variable ?
s is not valid
at that point you only have inserted   

if you want the fields then try

OUTPUT inserted.ID, inserted.[Field1], inserted.[Field2] 


instead of line 2 in your query.  You can find more here:

OUTPUT Clause (Transact-SQL)