Untitled

<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
    <title>Test Page</title>
    <link rel="stylesheet" type="text/css" href="../Content/bootstrap.css" />
    <link rel="stylesheet" type="text/css" href="//code.jquery.com/ui/1.11.4/themes/smoothness/jquery-ui.css" />
    <link rel="stylesheet" type="text/css" href="../Content/formValidation.min.css" />

    <script type="text/javascript" src="../Scripts/jquery-2.2.3.min.js"></script>
    <script type="text/javascript" src="../Scripts/jquery-ui-1.11.4.min.js"></script>
    <script type="text/javascript" src="../Scripts/bootstrap.min.js"></script>
    <script type="text/javascript" src="//momentjs.com/downloads/moment.min.js"></script>
    <script type="text/javascript" src="../Scripts/formValidation.popular.js"></script>
    <script type="text/javascript" src="../Scripts/framework/bootstrap.js"></script>
    <script type="text/javascript" src="../Scripts/bootbox.min.js"></script>
</head>
<body>
    <form id="form1" runat="server">
    <div>
        <label for="txtChildDOB1" class="control-label col-xs-1">DOB *</label>
        <div class="col-xs-1">
            <input type="date" class="form-control" style="position: absolute; z-index: 999" id="txtChildDOB1" name="txtChildDOB1" value="" runat="server" />
        </div>
    </div>
    </form>
</body>

protected void Page_Load(object sender, EventArgs e)
    {
        this.txtChildDOB1.Value = new DateTime(2002, 3, 19).ToShortDateString();
    }

<input type="date" id="datePicker" class="form-control" runat="server" />

<asp:TextBox TextMode="Date" ID="datePicker" class="form-control" runat="server" ></asp:TextBox>

string currentDate = DateTime.Now.ToString("yyyy") +
            "-" + DateTime.Now.ToString("MM") +
            "-" + DateTime.Now.ToString("dd");

datePicker.Value = today;