Check an example:
declare @date as date = ... some date ...
if DATEPART(day, @date) = 1 and DATEPART(month, @date) = DATEPART(month, GETDATE())
PRINT 'First day of current month'
if DATEPART(day, @date) = 1 and DATEPART(month, @date) = 1 and DATEPART(year, @date) = DATEPART(year, GETDATE())
PRINT 'First day of current year'
In case of current date:
declare @date as date = GETDATE()
if DATEPART(day, @date) = 1
PRINT 'First day of current month'
if DATEPART(day, @date) = 1 and DATEPART(month, @date) = 1
PRINT 'First day of current year'