Here is an example of how you can use the com.fasterxml.jackson.databind.introspect.AnnotatedConstructor class from the Jackson library in Java:

import com.fasterxml.jackson.annotation.JsonCreator;
import com.fasterxml.jackson.databind.ObjectMapper;
import com.fasterxml.jackson.databind.introspect.AnnotatedConstructor;

public class Example {
    public static void main(String[] args) {
        // Create an instance of the ObjectMapper class
        ObjectMapper mapper = new ObjectMapper();

        // Create an instance of the object you want to deserialize
        ExampleData data = new ExampleData("John Doe", 30);

        // Convert object to JSON string
        String json = mapper.writeValueAsString(data);
        System.out.println(json); // {"name":"John Doe","age":30}

        // Deserialize JSON string back to object
        ExampleData deserializedData = mapper.readValue(json, ExampleData.class);
        System.out.println(deserializedData.getName()); // "John Doe"
        System.out.println(deserializedData.getAge()); // 30

        // get the annotated constructor
        AnnotatedConstructor annotatedConstructor = mapper.getDeserializationConfig().introspect(ExampleData.class).getAnnotatedConstructor();
        if (annotatedConstructor != null) {
            // check if the constructor is annotated
            if (annotatedConstructor.hasAnnotation(JsonCreator.class)) {
                System.out.println("Annotated constructor found");
            }
        }
    }
}

class ExampleData {
    private String name;
    private int age;

    @JsonCreator
    public ExampleData(String name, int age) {
        this.name = name;
        this.age = age;
    }

    public String getName() { return name; }
    public void setName(String name) { this.name = name; }
    public int getAge() { return age; }
    public void setAge(int age) { this.age = age; }
}

This example uses the AnnotatedConstructor class to obtain the annotated constructor of the ExampleData class. To get the annotated constructor, it uses the getAnnotatedConstructor method of the com.fasterxml.jackson.databind.introspect.AnnotatedClass class, which is obtained via the com.fasterxml.jackson.databind.ObjectMapper.getDeserializationConfig().introspect(ExampleData.class) method.

In this example, the ExampleData class has an annotated constructor with @JsonCreator annotation.

Once you have obtained the annotated constructor, you can check whether it is annotated with the JsonCreator annotation, and do something accordingly.

Please note that this is just an example of how you might use this class, but you can use it for any other custom class in a similar way.