Selecting data between 2 date values using SQL and VB.NET

I'm fairly certain that SQL Server doesn't understand date literals like that. That would work for Access but different databases require different syntax. You should use text literals in yyyy-MM-dd format:

"' AND added_date BETWEEN '2020-07-21 00:00:00' AND '2020-07-21 23:59:59'"

That said, I'm guessing that you're going to have to vary those dates at some point, so you probably ought to be using parameters. You definitely should be using a parameter for the it_code value, e.g.

Dim sql = "SELECT sum(purchase_qty) FROM TB_STOCK WHERE it_code = @it_code AND added_date BETWEEN @added_date_start AND @added_date_end"
Dim command As New SqlCommand(sql, connection)

With command.Parameters
    .Add("@it_code", SqlDbType.VarChar, 50).Value = itCode
    .Add("@added_date_start", SqlDbType.DateTime).Value = myDate
    .Add("@added_date_end", SqlDbType.DateTime).Value = myDate.AddDays(1).AddSeconds(-1)
End With

I agree with Rodney Ellis about not using BETEWEEN too. I would do it like this:

Dim sql = "SELECT sum(purchase_qty) FROM TB_STOCK WHERE it_code = @it_code AND added_date >= @added_date_start AND added_date < @added_date_end"
Dim command As New SqlCommand(sql, connection)

With command.Parameters
    .Add("@it_code", SqlDbType.VarChar, 50).Value = itCode
    .Add("@added_date_start", SqlDbType.DateTime).Value = myDate
    .Add("@added_date_end", SqlDbType.DateTime).Value = myDate.AddDays(1)
End With

The last two examples both assume that myDate already has the time zeroed. If it doesn't, you can use myDate.Date.