Your Selected items must either be aggregates ( "SUM(Total_Amount)" for eg) or must be contained in the group by clause.
Date_Created != YEAR(Date_Created) or Month(Date_Created)
SELECT
YEAR(Date_Created),
Month(Date_Created),
SUM(Total_Amount)
FROM
dbo.FinalBillGenerated
where
YEAR(Date_Created)= 2016
group by
YEAR(Date_Created),
Month(Date_Created)