Hey maideen,
Create a list DateTime for holiday. Then check the DateTime with condition.
Please refer below sample.
HTML
StartDate :
<asp:TextBox runat="server" ID="txtStartDate" />
<br />
EndDate :<asp:TextBox runat="server" ID="txtEndDate" />
<br />
<asp:Button Text="Calculate" runat="server" OnClick="Calculate" />
Code
C#
protected void Calculate(object sender, EventArgs e)
{
    List<DateTime> holidays = new List<DateTime>();
    // Manually adding all holiday list.
    holidays.Add(new DateTime(DateTime.Now.Year, 1, 1)); // New Year.
    holidays.Add(new DateTime(DateTime.Now.Year, 1, 14)); // Makar Sankranti.
    holidays.Add(new DateTime(DateTime.Now.Year, 1, 26)); // National Holiday.
    DateTime startDate = Convert.ToDateTime(txtStartDate.Text);
    DateTime endDate = Convert.ToDateTime(txtEndDate.Text);
    int days = 0;
    for (DateTime date = startDate; date <= endDate; date = date.AddDays(1))
    {
        if (startDate.DayOfWeek != DayOfWeek.Saturday && startDate.DayOfWeek != DayOfWeek.Sunday && !holidays.Contains(date))
        {
            days++;
        }
        startDate = startDate.AddDays(1);
    }
    Response.Write("Number of days between " + Convert.ToDateTime(txtStartDate.Text).ToShortDateString() + " and "
        + Convert.ToDateTime(txtEndDate.Text).ToShortDateString() + " excluding special holiday is " + days.ToString());
}
VB.Net
Protected Sub Calculate(ByVal sender As Object, ByVal e As EventArgs)
    Dim holidays As List(Of DateTime) = New List(Of DateTime)()
    holidays.Add(New DateTime(DateTime.Now.Year, 1, 1))
    holidays.Add(New DateTime(DateTime.Now.Year, 1, 14))
    holidays.Add(New DateTime(DateTime.Now.Year, 1, 26))
    Dim startDate As DateTime = Convert.ToDateTime(txtStartDate.Text)
    Dim endDate As DateTime = Convert.ToDateTime(txtEndDate.Text)
    Dim days As Integer = 0
    Dim date1 As DateTime = startDate
    While date1 <= endDate
        If startDate.DayOfWeek <> DayOfWeek.Saturday AndAlso startDate.DayOfWeek <> DayOfWeek.Sunday AndAlso Not holidays.Contains(date1) Then
            days += 1
        End If
        startDate = startDate.AddDays(1)
        date1 = date1.AddDays(1)
    End While
    Response.Write("Number of days between " & Convert.ToDateTime(txtStartDate.Text).ToShortDateString() & " and " _
                   + Convert.ToDateTime(txtEndDate.Text).ToShortDateString() & " excluding special holiday is " + days.ToString())
End Sub
Screenshot
