There are various social media sharing plugins whose icons are sticky while scrolling down the screen in WordPress. You can see the working demo of a paid plugin named "WordPress Sticky Social Bar" at this page.
However, the social sharing media icons bar is fixed next to the right end of the browser in ths plugin. It's because it's easy to fix an element in this way in responsive themes. The CSS code like the following is used for this kind of effects.
.element_name { position: fixed; right: 0; top: 150px; }
In fact, it's easy to determine the position of a sticky element in non-responsive themes because the width of the content is fixed. However, it's difficult to make an element sticky in responsive sites.
Another WordPress Social Sharing plugin named "Socialsider - Universal Social Sidebar" adopts a similar method to make icons bar sticky.
How can fix an element next to the content area or sidebar in responsive WordPress themes? The following code snippets can be used.
position: fixed; top: 0; left: 50%; margin-left: 505px; margin-top: 225px; z-index: 100;
The following screenshot shows that social sharing icons are sticky next to the content area.
* For your reference, you might need to adjust the appearance of the sticky icons respectively for a disktop screen device and for a mobile screen device using media query.