Hi jain4,
I have created sample. Refer the below code.
<asp:DropDownCheckBoxes ID="DropDownCheckBoxes1" runat="server" UseSelectAllNode="false">
    <Style SelectBoxWidth="195" DropDownBoxBoxWidth="160" DropDownBoxBoxHeight="90" />
</asp:DropDownCheckBoxes>
 
<asp:ExtendedRequiredFieldValidator ID="ExtendedRequiredFieldValidator1" runat="server"
    ControlToValidate="DropDownCheckBoxes1" ErrorMessage="Required" ForeColor="Red">
</asp:ExtendedRequiredFieldValidator>
<br />
<br />
<asp:Button ID="Button1" Text="Submit" runat="server" OnClick="Submit" />
Code
string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        this.PopulateCountries();
    }
}
private void PopulateCountries()
{
    using (SqlConnection con = new SqlConnection(constr))
    {
        con.Open();
        using (SqlCommand cmd = new SqlCommand("SELECT ID,CountryName FROM Countries"))
        {
            cmd.CommandType = CommandType.Text;
            cmd.Connection = con;
            SqlDataAdapter sda = new SqlDataAdapter(cmd);
            using (DataTable dt = new DataTable())
            {
                sda.Fill(dt);
                DropDownCheckBoxes1.DataSource = dt;
                DropDownCheckBoxes1.DataTextField = "CountryName";
                DropDownCheckBoxes1.DataValueField = "ID";
                DropDownCheckBoxes1.DataBind();
            }
        }
        con.Close();
    }
    DataTable checkedCountries = GetCheckedCountries();
    if (checkedCountries != null)
    {
        foreach (ListItem item in DropDownCheckBoxes1.Items)
        {
            foreach (DataRow dr in checkedCountries.Rows)
            {
                if (dr["countryName"].ToString().Trim() == item.Text.Trim())
                {
                    item.Selected = true;
                }
            }
        }
    }
}
private DataTable GetCheckedCountries()
{
    DataTable dt;
    using (SqlConnection con = new SqlConnection(constr))
    {
        con.Open();
        using (SqlCommand cmd = new SqlCommand("SELECT prdID,countryName,CountryId FROM prdCountries"))
        {
            cmd.CommandType = CommandType.Text;
            cmd.Connection = con;
            SqlDataAdapter sda = new SqlDataAdapter(cmd);
            using (dt = new DataTable())
            {
                sda.Fill(dt);
            }
        }
        con.Close();
    }
    return dt;
}
protected void Submit(object sender, EventArgs e)
{
    foreach (ListItem item in DropDownCheckBoxes1.Items)
    {
        if (item.Selected)
        {
            InsertprdCountry(item.Text.Trim(), item.Value.Trim());
        }
    }
    ClientScript.RegisterClientScriptBlock(this.GetType(), "alert", "alert('Record inserted successfully.');", true);
}
protected void InsertprdCountry(string countryName, string CountryId)
{
    using (SqlConnection con = new SqlConnection(constr))
    {
        using (SqlCommand cmd = new SqlCommand("INSERT INTO prdCountries (countryName, CountryId) values (@countryName, @CountryId)"))
        {
            cmd.CommandType = CommandType.Text;
            cmd.Parameters.AddWithValue("@countryName", countryName);
            cmd.Parameters.AddWithValue("@CountryId", CountryId);
            cmd.Connection = con;
            con.Open();
            cmd.ExecuteNonQuery();
            con.Close();
        }
    }
}