As far as I know Ashley does not have any pre-built systems that would handle click events and map them to entities.

A simple clickable system could easily be created using a clickable component and clickable system.

An example with an OrthographicCamera:

The clickable component with the rectangle bounds

public class ClickableComponent implements Component{
    public Rectangle bounds = new Rectangle(0,0,10,10);
}

A Transform component to store location

public class TransformComponent implements Component{
    public final Vector3 position = new Vector3();
}

With a Clickable System

public class ClickableSystem extends IteratingSystem{

    private ComponentMapper<ClickableComponent> cc;
    private ComponentMapper<TransformComponent> tc;
    private OrthographicCamera camera;
    
    
    @SuppressWarnings("unchecked")
    public ClickableSystem(OrthographicCamera cam) {
        super(Family.all(ClickableComponent.class,TransformComponent.class).get());
        cc = ComponentMapper.getFor(ClickableComponent.class);
        tc = ComponentMapper.getFor(TransformComponent.class);
        camera = cam;
    }
    
    @Override
    protected void processEntity(Entity entity, float deltaTime) {
        ClickableComponent click = cc.get(entity);
        TransformComponent transform = tc.get(entity);
        
        //update click bounds
        click.bounds.x = transform.position.x;
        click.bounds.y = transform.position.y;
        
        if(Gdx.input.isButtonPressed(Buttons.LEFT)){
            // touching
            Vector3 clickPosition = camera.unproject(new Vector3(Gdx.input.getX(), Gdx.input.getY(),0));
            System.out.println(clickPosition+":"+click.bounds.toString());
            if(click.bounds.contains(clickPosition.x, clickPosition.y)){
                //object clicked
                //do your thing
                System.out.println("Touched"+entity.toString());
            }
        }
    }
}