How to get count of 2nd and 4th Saturday's exactly between 2 dates using sql query

I use a UDF to create dynamic date ranges, but a Tally/Date Table would do the trick as well

with cteBase as (
    Select * 
          ,RowNr=Row_Number() over (Order by RetVal)
      From [dbo].[udf-Create-Range-Date]('2016-08-01','2016-09-20','DD',1) 
      Where DateName(DW,RetVal)='Saturday'
)
Select RetVal From cteBase Where RowNr in (2,4)

Returns

RetVal
2016-08-13 00:00:00.000
2016-08-27 00:00:00.000

The UDF if needed

CREATE FUNCTION [dbo].[udf-Create-Range-Date] (@DateFrom datetime,@DateTo datetime,@DatePart varchar(10),@Incr int)

Returns 
@ReturnVal Table (RetVal datetime)

As
Begin
    With DateTable As (
        Select DateFrom = @DateFrom
        Union All
        Select Case @DatePart
               When 'YY' then DateAdd(YY, @Incr, df.dateFrom)
               When 'QQ' then DateAdd(QQ, @Incr, df.dateFrom)
               When 'MM' then DateAdd(MM, @Incr, df.dateFrom)
               When 'WK' then DateAdd(WK, @Incr, df.dateFrom)
               When 'DD' then DateAdd(DD, @Incr, df.dateFrom)
               When 'HH' then DateAdd(HH, @Incr, df.dateFrom)
               When 'MI' then DateAdd(MI, @Incr, df.dateFrom)
               When 'SS' then DateAdd(SS, @Incr, df.dateFrom)
               End
        From DateTable DF
        Where DF.DateFrom < @DateTo
    )

    Insert into @ReturnVal(RetVal) Select DateFrom From DateTable option (maxrecursion 32767)

    Return
End

-- Syntax Select * from [dbo].[udf-Create-Range-Date]('2016-10-01','2020-10-01','YY',1) 
-- Syntax Select * from [dbo].[udf-Create-Range-Date]('2016-10-01','2020-10-01','DD',1) 
-- Syntax Select * from [dbo].[udf-Create-Range-Date]('2016-10-01','2016-10-31','MI',15) 
-- Syntax Select * from [dbo].[udf-Create-Range-Date]('2016-10-01','2016-10-02','SS',1) 

EDIT to Return Every OTHER Saturday within Range

with cteBase as (
    Select * 
          ,RowNr=Row_Number() over (Order by RetVal)
      From [dbo].[udf-Create-Range-Date]('2016-09-17','2016-10-29','DD',1)
      Where DateName(DW,RetVal)='Saturday'
)
Select RetVal From cteBase Where RowNr % 2 = 0

Returns

RetVal
2016-09-24 00:00:00.000
2016-10-08 00:00:00.000
2016-10-22 00:00:00.000