JSFiddle - React, Tailwind, and code Playground

HTML

<!--fixedmenu.begin-->
	<nav id="fixed-header" class="default">
		<ul>
			<li><a href="#">Почему мы</a>
			<li><a href="#">Коротко о нас</a>			
			<li><a href="#">Наш центр</a>
			<li><a href="#">Контакты</a>
		</ul>
	</nav>
	<!--fixedmenu.end-->
                
    <section></section>

CSS

*{
    padding: 0;
    margin: 0;
    font-family: sans-serif;
}


#fixed-header.default {
	display: none; 
} 
#fixed-header.fixed {
	position: fixed;
	min-height: 30px;	
	width: 100%;
	text-align: center;
	background: #fff;
	background: rgba(255,255,255,0.85);
	z-index: 2000;
	-webkit-box-shadow: 0 6px 4px -4px rgba(0,0,0,0.2);
	-moz-box-shadow: 0 6px 4px -4px rgba(0,0,0,0.2);
	box-shadow: 0 6px 4px -4px rgba(0,0,0,0.2);
}
nav ul{	
	font-size: 0;	
}
nav ul li{
    font-size: 16px;
	display: inline-block;
	*display: inline;
	zoom: 1;
	vertical-align: middle;	
	-moz-box-sizing: border-box; 
	box-sizing: border-box; 
}
nav ul li a{	
	display: inline-block;
	*display: inline;
	zoom: 1;
    color: #353535;
	text-decoration: none;
	padding: 5px 15px;
}
nav ul li a:hover{
	color: #fff;		 
	background: #70B908;
}


section{
    min-height: 2000px;
    background: #000;
}

JavaScript

$(document).ready(function(){
 
        var $menu = $("#fixed-header");
 
        $(window).scroll(function(){
            if ( $(this).scrollTop() > 300 && $menu.hasClass("default") ){
                $menu.fadeIn(500).removeClass("default").addClass("fixed");
            } else if($(this).scrollTop() <= 300 && $menu.hasClass("fixed")) {
                $menu.fadeOut(0).removeClass("fixed").addClass("default");
            }
        });
    });