Hi SaChie,
Please take reference the below code and  correct your code.
HTML
<div>
    Name:
    <asp:TextBox ID="txtName" runat="server"></asp:TextBox>
    <asp:RequiredFieldValidator ID="rfvtxtName" runat="server" ControlToValidate="txtName"
        ErrorMessage="Please Enter Name"></asp:RequiredFieldValidator>
    <br />
    <asp:Button ID="btnValidate" runat="server" Text="Submit" OnClientClick="Validate();" />
</div>
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
<script type="text/javascript">
    function Validate() {
        var name = document.getElementById("txtName").value;
        if (name == "") {
            $("#txtName").css("border", "1px solid red");
            $("#txtName").focus();
        }
    }
</script>
Screenshot
