Hi nauna,

Check this example. Now please take its reference and correct your code.

Database

CREATE TABLE tblTimes
(
    Id INT IDENTITY PRIMARY KEY,
    Time VARCHAR(10)
)

INSERT INTO tblTimes VALUES
('12:00 PM'),('02:00 PM'),('05:00 PM'),
('07:00 PM'),('08:00 AM'),('10:00 AM')

SELECT * FROM tblTimes

HTML

<asp:TextBox ID="TextBox1" runat="server" TextMode="Date"
    OnTextChanged="DateChanged" AutoPostBack="true"></asp:TextBox>
<asp:DropDownList runat="server" ID="ddlTimes">
</asp:DropDownList>

Code

C#

protected void DateChanged(object sender, EventArgs e)
{
    DateTime selectedDate = Convert.ToDateTime(TextBox1.Text.Trim());
    List<ListItem> times = GetTime();
    for (int i = times.Count; i > 0; --i)
    {
        DateTime dt;
        if (!DateTime.TryParse(times[i - 1].Text, out dt)) { }

        if (dt <= DateTime.Now && selectedDate == DateTime.Today)
        {
            times.RemoveAt(i - 1);
        }
    }
    ddlTimes.DataSource = times;
    ddlTimes.DataTextField = "Text";
    ddlTimes.DataValueField = "Value";
    ddlTimes.DataBind();
}

private List<ListItem> GetTime()
{
    List<ListItem> times = new List<ListItem>();
    string conString = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
    string query = "SELECT * FROM tblTimes";
    using (SqlConnection con = new SqlConnection(conString))
    {
        SqlCommand cmd = new SqlCommand(query, con);
        con.Open();
        SqlDataReader sdr = cmd.ExecuteReader();
        while (sdr.Read())
        {
            times.Add(new ListItem()
            {
                Text = Convert.ToDateTime(sdr["Time"]).ToString("hh:mm tt"),
                Value = Convert.ToDateTime(sdr["Time"]).ToString("hh:mm tt")
            });
        }
        con.Close();
    }

    return times;
}

VB.Net

    Protected Sub DateChanged(ByVal sender As Object, ByVal e As EventArgs)
        Dim selectedDate As DateTime = Convert.ToDateTime(TextBox1.Text.Trim())
        Dim times As List(Of ListItem) = GetTime()
        For i As Integer = times.Count To 1 Step -1
            Dim dt As DateTime
            If Not DateTime.TryParse(times(i - 1).Text, dt) Then
            End If
            If dt <= DateTime.Now AndAlso selectedDate = DateTime.Today Then
                times.RemoveAt(i - 1)
            End If
        Next

        ddlTimes.DataSource = times
        ddlTimes.DataTextField = "Text"
        ddlTimes.DataValueField = "Value"
        ddlTimes.DataBind()
    End Sub

    Private Function GetTime() As List(Of ListItem)
        Dim times As List(Of ListItem) = New List(Of ListItem)()
        Dim conString As String = ConfigurationManager.ConnectionStrings("constr").ConnectionString
        Dim query As String = "SELECT * FROM tblTimes"
        Using con As SqlConnection = New SqlConnection(conString)
            Dim cmd As SqlCommand = New SqlCommand(query, con)
            con.Open()
            Dim sdr As SqlDataReader = cmd.ExecuteReader()
            While sdr.Read()
                times.Add(New ListItem() With {
                    .Text = Convert.ToDateTime(sdr("Time")).ToString("hh:mm tt"),
                    .Value = Convert.ToDateTime(sdr("Time")).ToString("hh:mm tt")
                })
            End While
            con.Close()
        End Using

        Return times
    End Function

Screenshot