Hi nedash,
Refer the below code.
HTML
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
<title></title>
<style type="text/css">
#ddlColor option:hover
{
background-color: Red;
}
</style>
</head>
<body>
<form id="form1" runat="server">
<div>
<select name="ddlColor" id="ddlColor">
<option value="Red">Red</option>
<option value="Orange">Orange</option>
<option value="Yellow">Yellow</option>
<option value="Green">Green</option>
</select>
</div>
</form>
</body>
</html>
Demo
HTML
<div>
<asp:DropDownList ID="ddlmostanad" runat="server" CssClass="ddlSmostanad">
<asp:ListItem Text="text 1" />
<asp:ListItem Text="text 2" />
<asp:ListItem Text="text 3" />
<asp:ListItem Text="text 4" />
<asp:ListItem Text="text 5" />
</asp:DropDownList>
</div>
<div>
<style type="text/css">
#ddlmostanad option:hover
{
background-color: red;
}
</style>
</div>
Screenshot
Note: It will work only in IE and Microsoft Edge. It will not work for chrome and mozilla because they have inbuilt hover textcolor.