How to autogenerate created or modified timestamp field?

You can go with Spring Data JPA, Spring has made it as easy using annotation @CreatedBy, @CreatedDate, @LastModifiedBy, @LastModifiedDate on your fields. You can follow below simple example

// Will need to enable JPA Auditing
@Configuration
@EnableJpaAuditing(auditorAwareRef = "auditorAware")
class JpaConfig {
    // Creating a bean of AuditorAwareImpl which will provide currently logged in user
    @Bean
    public AuditorAware<String> auditorAware() {
        return new AuditorAwareImpl();
    }
}

// Moving necessary fields to super class and providing AuditingEntityListener entity listner class
@MappedSuperclass
@EntityListeners(AuditingEntityListener.class)
abstract class Auditable<U> {

    @CreatedBy
    protected U createdBy;

    @CreatedDate
    @Temporal(TIMESTAMP)
    protected Date createdDate;

    @LastModifiedBy
    protected U lastModifiedBy;

    @LastModifiedDate
    @Temporal(TIMESTAMP)
    protected Date lastModifiedDate;

    // Getters and Setters
}

// Creating implementation of AuditorAware and override its methods to provide currently logged in user
class AuditorAwareImpl implements AuditorAware<String> {

    @Override
    public String getCurrentAuditor() {
        return "Naresh";
        // Can use Spring Security to return currently logged in user
        // return ((User) SecurityContextHolder.getContext().getAuthentication().getPrincipal()).getUsername()
    }
}

@Entity
class File extends Auditable<String> {
    @Id
    @GeneratedValue
    private Integer id;
    private String name;
    private String content;

    // Getters and Setters
} 

You can read more on my article Spring Data JPA Auditing: Saving CreatedBy, CreatedDate, LastModifiedBy, LastModifiedDate automatically for more details.

You can just create a new Date() whenever your instance is created, and then update the updated field whenever the entity gets updated:

private Date created = new Date();
private Date updated = new Date();

@PreUpdate
public void setLastUpdate() {  this.updated = new Date(); }

Don't provide a setter for any of these methods, only getters.

In 4.3 Hibernate with JPA, one can use "@CreationTimestamp" and "@UpdateTimestamp" directly in the date fields

CreationTimestamp java doc

UpdateTimestamp java doc

We do this with a PreInsertEventListener and a PreUpdateEventListener :

public class TracabilityListener implements PreInsertEventListener,PreUpdateEventListener {
    private void setPropertyState(Object[] propertyStates, String[] propertyNames,String propertyName,Object propertyState) {
        for(int i=0;i<propertyNames.length;i++) {
            if (propertyName.equals(propertyNames[i])) {
                propertyStates[i]=propertyState;
                return;
            }
        }
    }
    private void onInsert(Object entity,Object[] state, String[] propertyNames) {
        if (entity instanceof DomainObject) {
            DomainObject domainObject = (DomainObject) entity;
            Date date=new Date();
            domainObject.setDateCreation(date);
            setPropertyState(state, propertyNames, "dateCreation", date);
            domainObject.setDateModification(date);
            setPropertyState(state, propertyNames, "dateModification", date);
        }
    }

    private void onUpdate(Object entity,Object[] state, String[] propertyNames) {
        if (entity instanceof DomainObject) {
            DomainObject domainObject = (DomainObject) entity;
            Date date=new Date();
            setPropertyState(state, propertyNames, "dateCreation", domainObject.getDateCreation());
            domainObject.setDateModification(date);
            setPropertyState(state, propertyNames, "dateModification", date);
        }
    }

    @Override
    public boolean onPreInsert(PreInsertEvent event) {
        onInsert(event.getEntity(), event.getState(), event.getPersister().getPropertyNames());
        return false;
    }

    @Override
    public boolean onPreUpdate(PreUpdateEvent event) {
        onUpdate(event.getEntity(), event.getState(), event.getPersister().getPropertyNames());
        return false;
    }
}

But if you want your properties to be timestamps, then they should be annotated with

@Temporal(TemporalType.TIMESTAMP)