Q:

Anchor link takes two clicks to fire the event

The HTML:
<asp:TextBox ID="dataTextBox" MaxLength="10" runat="server"></asp:TextBox>

<a class='new_message' onclick='focusMethod();' tabindex='-1' href='#dataTextBox"> New Message</a>";

Jquery function:
function focusMethod() {
        $('[class=new_message]').click(function (e) {
            e.preventDefault();
            $($(this).attr('href')).focus();
        });
    }

When i click the anchor link the focus should go to the input text box. But it is taking 2 clicks to perform. 
My scenarios are:

onclick is used in anchor tag to prevent default behaviour i.e firing the href.
I am building an accessible form so i need the href with value (so i wont be able to use href="#")
If i use just the click event handler without the function it is not being fired( instead href is fired and focus is not going to textbox)

It takes 2 clicks because the function focusMethod is fired first and then event handler is attached.
Is there any way to avoid performing the function "focusmethod' and only perform click event handler?

A:

Because your method focusMethod is binding a new click event which is then executing next time you click that element. Just remove the inline click event onclick='focusMethod();' as it's not needed. Then instead of a function you can just do:
$('[class=new_message]').click(function (e) {
    e.preventDefault();
    $($(this).attr('href')).focus();
});

Edit:
Since your element is dynamic you need to use $(document).on(...) instead, otherwise the selector $(...).click(..) isn't going to find the element as it wouldn't exist when setting up the click event binding.
Below is a basic example with the element being dynamically created:

$(document).on("click", "[class=new_message]", function (e) {
    e.preventDefault();
    console.log("clicked");
    $($(this).attr('href')).focus();
});

$("body").html("<a class='new_message' tabindex='-1' href='#dataTextBox'> New Message</a>");
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>

