Drag spinner from its textfield:

import javafx.application.Application;
import javafx.scene.Scene;
import javafx.scene.control.Spinner;
import javafx.scene.control.SpinnerValueFactory;
import javafx.scene.layout.VBox;
import javafx.stage.Stage;

public class DraggableSpinnerApp extends Application {

    @Override
    public void start(Stage primaryStage) {
        Spinner<Integer> spinner = new Spinner<>();
        
        SpinnerValueFactory<Integer> valueFactory = new SpinnerValueFactory.IntegerSpinnerValueFactory(Integer.MIN_VALUE, Integer.MAX_VALUE, 0);
        spinner.setValueFactory(valueFactory);
        // There will be a little conflict between text selection and dragging
        spinner.setEditable(true);
        
        final double[] mouseAnchorY = {0d};
        final double[] spinnerValOnStartDrag = {0d};
        
        spinner.getEditor().setOnMousePressed(event -> {
            // Capture the starting Y position and spinner value
            mouseAnchorY[0] = event.getSceneY();
            spinnerValOnStartDrag[0] = spinner.getValue();
        });

        // Mouse dragged event to calculate new value
        spinner.getEditor().setOnMouseDragged(event -> {
            double deltaY = mouseAnchorY[0] - event.getSceneY(); // Calculate the delta

            // Observe values in console
            System.out.printf("%s %s %s delta=%s%n",mouseAnchorY[0],event.getSceneY(),event.getEventType(),deltaY);
            
            // For bigger initial values we want proportionally big delta factor
            var valAbs = Math.abs(spinnerValOnStartDrag[0]);
            var factor = String.valueOf(valAbs).length();
            
            int newValue = (int) (spinnerValOnStartDrag[0]+deltaY*factor);
            spinner.getValueFactory().setValue(newValue);
        });
        

        VBox vbox = new VBox(spinner);
        Scene scene = new Scene(vbox, 400, 200);
        primaryStage.setScene(scene);
        primaryStage.setTitle("Draggable Spinner Example");
        primaryStage.show();
    }

    public static void main(String[] args) {
        launch(args);
    }
}

Maybe it would be better to bind this listener to buttons instead.