<UserControl x:Name="userControl" x:Class="Test_Paramaterized_UserControl_with_MVVM.UserControl1"
             xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
             xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
             xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
             xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
             xmlns:local="clr-namespace:Test_Paramaterized_UserControl_with_MVVM"
             xmlns:view="clr-namespace:Daavlin.SmartTouch.STUV_WPF.View"
             mc:Ignorable="d"
             d:DesignHeight="300" d:DesignWidth="300">
      <Grid Margin="10">
        <Border BorderThickness="3" BorderBrush="Black" Padding="10">
            <StackPanel HorizontalAlignment="Center" VerticalAlignment="Center">
                <StackPanel Orientation="Horizontal">
                    <TextBlock Text="UserControl1 View: "/>
                    <TextBlock Text="{Binding ElementName=userControl, Path=PropUserControlView, Mode=OneWay}" FontWeight="Bold"/>
                </StackPanel>
                <Rectangle Height="5"/>
                <StackPanel Orientation="Horizontal">
                    <TextBlock Text="UserControl1 ViewModel: " />
                    <TextBlock Text="{Binding PropUserControlViewModel, FallbackValue=propUserControlViewModel 2}" FontWeight="Bold">
                        <TextBlock.DataContext>
                            <local:UserControl1ViewModel/>
                        </TextBlock.DataContext>
                    </TextBlock>
                </StackPanel>
            </StackPanel>
        </Border>
    </Grid>
</UserControl>

public partial class UserControl1 : UserControl
    {
        public UserControl1()
        {
            InitializeComponent();
        }

        public string PropUserControlView { get => (string)GetValue(PropUserControlViewProperty); set => SetValue(PropUserControlViewProperty, value); }
        public static readonly DependencyProperty PropUserControlViewProperty =
            DependencyProperty.Register(nameof(PropUserControlView), typeof(string), typeof(UserControl1),
                new PropertyMetadata(null, DependencyPropertyChanged));

        private static void DependencyPropertyChanged(DependencyObject dependencyObject, DependencyPropertyChangedEventArgs dependencyPropertyChangedEventArgs)
        {
            var x = dependencyPropertyChangedEventArgs.NewValue;
        }
    }

    public class UserControl1ViewModel : ObservableObject
    {
        public string PropUserControlViewModel { get => _propUserControlViewModel; set => SetField(ref _propUserControlViewModel, value); }
        private string _propUserControlViewModel = "value from UserControl-ViewModel";
    }

<Window x:Class="Test_Paramaterized_UserControl_with_MVVM.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:local="clr-namespace:Test_Paramaterized_UserControl_with_MVVM"
        Title="MainWindow" >
    <Window.DataContext>
        <local:MainWindowViewModel />
    </Window.DataContext>
    <Grid VerticalAlignment="Top" >
        <StackPanel VerticalAlignment="Center" HorizontalAlignment="Center" Margin="20">
            <StackPanel Orientation="Horizontal">
                <TextBlock Text="MainWindow1 ViewModel: "/>
                <TextBox Text="{Binding PropWindowViewModel, UpdateSourceTrigger=PropertyChanged}" FontWeight="Bold"/>
            </StackPanel>
            <Rectangle Height="10"/>
            <StackPanel Orientation="Horizontal">
                <TextBlock Text="UserControl1 (fixed value Fixed): " VerticalAlignment="Center"/>
                <local:UserControl1 PropUserControlView="Fixed"/>
            </StackPanel>
            <!--<Rectangle Height="10"/>
            <StackPanel Orientation="Horizontal">
                <TextBlock Text="UserControl1 (bound to MainWindows VM via binding Path): " VerticalAlignment="Center"/>
                <local:UserControl1 PropUserControlView="{Binding ElementName=MainWindow1, Path=DataContext.PropWindowViewModel}"/>
            </StackPanel>-->
            <Rectangle Height="10"/>
            <StackPanel Orientation="Horizontal">
                <TextBlock Text="UserControl1 (bound to MainWindows VM): " VerticalAlignment="Center"/>
                <local:UserControl1 PropUserControlView="{Binding PropWindowViewModel}"/>
            </StackPanel>
        </StackPanel>
    </Grid>
</Window>

public partial class MainWindow : Window
{
    public MainWindow()
    {
        InitializeComponent();
    }
}

public class MainWindowViewModel : ObservableObject
{
    public string PropWindowViewModel { get => _propWindowViewModel; set => SetField(ref _propWindowViewModel, value); }
    private string _propWindowViewModel = "valuefrom Window-VIewModel";
}