This is a servlet which return true or false, if the AEM run mode is publish or not.

RunModeServlet.java

import org.apache.sling.api.SlingHttpServletRequest;
import org.apache.sling.api.SlingHttpServletResponse;
import org.apache.sling.api.servlets.SlingAllMethodsServlet;
import org.apache.sling.settings.SlingSettingsService;
import org.osgi.service.component.annotations.Component;
import org.osgi.service.component.annotations.Reference;

import javax.servlet.Servlet;
import java.io.IOException;

@Component(
        service = {Servlet.class},
        property = {
                "sling.servlet.paths=/bin/aem-integration/tasks",
                "sling.servlet.paths=/bin/aem-integration/files",
                "sling.servlet.extensions=json",
                "sling.servlet.methods=GET"
        }
)
public class RunModeServlet extends SlingAllMethodsServlet {

    @Reference
    private SlingSettingsService slingSettingsService;

    @Override
    protected void doGet(SlingHttpServletRequest request, SlingHttpServletResponse response) throws IOException {
        response.getWriter().println(this.slingSettingsService.getRunModes().contains("publish"));
    }
}