public class MyPopup : Popup
{
    static MyPopup()
    {
        DefaultStyleKeyProperty.OverrideMetadata(typeof(MyPopup), new FrameworkPropertyMetadata(typeof(MyPopup)));
    }
}

<Style x:Key="MyPopupStyle" TargetType="{x:Type local:MyPopup}">
    <Setter Property="Placement" Value="MousePoint" />
    <Setter Property="Child">
        <Setter.Value>
            <Border
                Width="100"
                Height="100"
                Background="HotPink" />
        </Setter.Value>
    </Setter>
    <Setter Property="IsOpen" Value="{Binding RelativeSource={RelativeSource Self}, Path=PlacementTarget.IsMouseOver, Mode=OneWay}" />
</Style>

<Window.Resources>
    <DataTemplate x:Key="Foo">
        <StackPanel HorizontalAlignment="Center" VerticalAlignment="Center">
            <TextBlock x:Name="TextBlock" Text="Hover over" />
            <wpfApp1:MyPopup PlacementTarget="{Binding ElementName=TextBlock}" />
        </StackPanel>
    </DataTemplate>
 </Window.Resources>
 <ListBox ItemTemplate="{StaticResource Foo}" ItemsSource="{Binding MyList}" />

public partial class MainWindow
{
    public MainWindow()
    {
        InitializeComponent();
        MyList = new List<string>{"Dan","John","Test"};
        DataContext = this;
    }
    public List<string> MyList { get; }
}