[html] How to change the style of the title attribute inside an anchor tag?

You can't style an actual title attribute

How the text in the title attribute is displayed is defined by the browser and varies from browser to browser. It's not possible for a webpage to apply any style to the tooltip that the browser displays based on the title attribute.

However, you can create something very similar using other attributes.

You can make a pseudo-tooltip with CSS and a custom attribute (e.g. data-title)

For this, I'd use a data-title attribute. data-* attributes are a method to store custom data in DOM elements/HTML. There are multiple ways of accessing them. Importantly, they can be selected by CSS.

Given that you can use CSS to select elements with data-title attributes, you can then use CSS to create :after (or :before) content that contains the value of the attribute using attr().

Styled tooltip Examples

Bigger and with a different background color (per question's request):

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[data-title]:hover:after {_x000D_
    opacity: 1;_x000D_
    transition: all 0.1s ease 0.5s;_x000D_
    visibility: visible;_x000D_
}_x000D_
[data-title]:after {_x000D_
    content: attr(data-title);_x000D_
    background-color: #00FF00;_x000D_
    color: #111;_x000D_
    font-size: 150%;_x000D_
    position: absolute;_x000D_
    padding: 1px 5px 2px 5px;_x000D_
    bottom: -1.6em;_x000D_
    left: 100%;_x000D_
    white-space: nowrap;_x000D_
    box-shadow: 1px 1px 3px #222222;_x000D_
    opacity: 0;_x000D_
    border: 1px solid #111111;_x000D_
    z-index: 99999;_x000D_
    visibility: hidden;_x000D_
}_x000D_
[data-title] {_x000D_
    position: relative;_x000D_
}
_x000D_
<a href="example.com" data-title="My site"> Link </a> with styled tooltip (bigger and with a different background color, as requested in the question)<br/>_x000D_
<a href="example.com" title="My site"> Link </a> with normal tooltip
_x000D_
_x000D_
_x000D_

More elaborate styling (adapted from this blog post):

_x000D_
_x000D_
[data-title]:hover:after {_x000D_
    opacity: 1;_x000D_
    transition: all 0.1s ease 0.5s;_x000D_
    visibility: visible;_x000D_
}_x000D_
[data-title]:after {_x000D_
    content: attr(data-title);_x000D_
    position: absolute;_x000D_
    bottom: -1.6em;_x000D_
    left: 100%;_x000D_
    padding: 4px 4px 4px 8px;_x000D_
    color: #222;_x000D_
    white-space: nowrap; _x000D_
    -moz-border-radius: 5px; _x000D_
    -webkit-border-radius: 5px;  _x000D_
    border-radius: 5px;  _x000D_
    -moz-box-shadow: 0px 0px 4px #222;  _x000D_
    -webkit-box-shadow: 0px 0px 4px #222;  _x000D_
    box-shadow: 0px 0px 4px #222;  _x000D_
    background-image: -moz-linear-gradient(top, #f8f8f8, #cccccc);  _x000D_
    background-image: -webkit-gradient(linear,left top,left bottom,color-stop(0, #f8f8f8),color-stop(1, #cccccc));_x000D_
    background-image: -webkit-linear-gradient(top, #f8f8f8, #cccccc);  _x000D_
    background-image: -moz-linear-gradient(top, #f8f8f8, #cccccc);  _x000D_
    background-image: -ms-linear-gradient(top, #f8f8f8, #cccccc);  _x000D_
    background-image: -o-linear-gradient(top, #f8f8f8, #cccccc);_x000D_
    opacity: 0;_x000D_
    z-index: 99999;_x000D_
    visibility: hidden;_x000D_
}_x000D_
[data-title] {_x000D_
    position: relative;_x000D_
}
_x000D_
<a href="example.com" data-title="My site"> Link </a> with styled tooltip<br/>_x000D_
<a href="example.com" title="My site"> Link </a> with normal tooltip
_x000D_
_x000D_
_x000D_

Known issues

Unlike a real title tooltip, the tooltip produced by the above CSS is not, necessarily, guaranteed to be visible on the page (i.e. it might be outside the visible area). On the other hand, it is guaranteed to be within the current window, which is not the case for an actual tooltip.

In addition, the pseudo-tooltip is positioned relative to the element that has the pseudo-tooltip rather than relative to where the mouse is on that element. You may want to fine-tune where the pseudo-tooltip is displayed. Having it appear in a known location relative to the element can be a benefit or a drawback, depending on the situation.

You can't use :before or :after on elements which are not containers

There's a good explanation in this answer to "Can I use a :before or :after pseudo-element on an input field?"

Effectively, this means that you can't use this method directly on elements like <input type="text"/>, <textarea/>, <img>, etc. The easy solution is to wrap the element that's not a container in a <span> or <div> and have the pseudo-tooltip on the container.

Examples of using a pseudo-tooltip on a <span> wrapping a non-container element:

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_x000D_
[data-title]:hover:after {_x000D_
    opacity: 1;_x000D_
    transition: all 0.1s ease 0.5s;_x000D_
    visibility: visible;_x000D_
}_x000D_
[data-title]:after {_x000D_
    content: attr(data-title);_x000D_
    background-color: #00FF00;_x000D_
    color: #111;_x000D_
    font-size: 150%;_x000D_
    position: absolute;_x000D_
    padding: 1px 5px 2px 5px;_x000D_
    bottom: -1.6em;_x000D_
    left: 100%;_x000D_
    white-space: nowrap;_x000D_
    box-shadow: 1px 1px 3px #222222;_x000D_
    opacity: 0;_x000D_
    border: 1px solid #111111;_x000D_
    z-index: 99999;_x000D_
    visibility: hidden;_x000D_
}_x000D_
[data-title] {_x000D_
    position: relative;_x000D_
}_x000D_
_x000D_
.pseudo-tooltip-wrapper {_x000D_
    /*This causes the wrapping element to be the same size as what it contains.*/_x000D_
    display: inline-block;_x000D_
}
_x000D_
Text input with a pseudo-tooltip:<br/>_x000D_
<span class="pseudo-tooltip-wrapper" data-title="input type=&quot;text&quot;"><input type='text'></span><br/><br/><br/>_x000D_
Textarea with a pseudo-tooltip:<br/>_x000D_
<span class="pseudo-tooltip-wrapper" data-title="this is a textarea"><textarea data-title="this is a textarea"></textarea></span><br/>
_x000D_
_x000D_
_x000D_


From the code on the blog post linked above (which I first saw in an answer here that plagiarized it), it appeared obvious to me to use a data-* attribute instead of the title attribute. Doing so was also suggested in a comment by snostorm on that (now deleted) answer.