JSFiddle - React, Tailwind, and code Playground

HTML

<ul class="sub-menu">
    <li>This is option one.</li>
    <li>This is a second option.</li>
    <li>We'll need three.</li>
    <li>And now these are out of view.</li>
    <li>I'm the last option.</li>
</ul>

CSS

.sub-menu {
    padding: 0;
    border: 1px solid black;
    max-height: 4.5em;
    overflow-y: auto;
}

.sub-menu li {
    font-size: 1em;
    padding: .25em 1em;
    line-height: 1em;
}

.sub-menu li:hover {
    background: #f1f1f1;
}