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To use styles for your custom usercontrol, you have to define the styles TargetType property with an x:Type in your resource dictionary.

<ResourceDictionary
    xmlns="http://xamarin.com/schemas/2014/forms"
    xmlns:x="http://schemas.microsoft.com/winfx/2009/xaml"
    xmlns:buttons="clr-namespace:AnAwesomeApp.Controls.Buttons"
    x:Class="AnAwesomeApp.Resources.Styles">

Declare the clr-namespace where your custom usercontrol lives.

<Style
        x:Key="BlueButtonStyle"
        TargetType="{x:Type buttons:ColoredButton}">
        <Setter
            Property="TextColor"
            Value="White" />
        <Setter
            Property="Color"
            Value="{AppThemeBinding Dark=#2325A6, Light=#61BAFF}" />
        <Setter
            Property="FontFamily"
            Value="Nunito" />
    </Style>

Set the target type with x:Type.

And boom, done!