Is there way (public API preferably) to fetch list of CI's related to application service (like "List CIs" link behavior on business service display page)?

[Pratiksha7]

Business service display page has a link with caption "List CIs". This link when clicked returns related CI list. I want to fetch such list using API or Script. But I couldn't find any public API for the same. I also tried to write script but it returns way more CI's than I am interested in. Is there a away to fetch exact list of CI's returned by "List CIs" link which makes following REST call :
https://devxxxxx.service-now.com/cmdb_ci_list.do?sysparm_query=sys_idINjavascript:saListCis('sys_id')

While "ListCIs" link returns only 11 CIs, my script returns 676 CIs (when break condition is on 100 level).

My scirpt:
var sys_id = g_request.getParameter("systemId");
var record  = new GlideRecord('cmdb_rel_ci');
var childList = [];
var i = 0;
childList.push(sys_id);
while(i < childList.length) {
record = new GlideRecord('cmdb_rel_ci');
record.addQuery('parent', childList[i]);
g_processor.writeOutput("text/plain", "\n\nCalling for " + i + "\t value : " + childList[i] + "\t length : " + childList.length);
record.query();
record.getAttribute();
var relId = "";
while (record.next()) {
    relId = record.getValue("sys_id");
    childList.push(record.child.toString());
}
if(relId == "")
    g_processor.writeOutput("text/plain", "\tDetails not found for: " + childList[i]);
i++;
    if( i > 100)
        break;
}

Do we need to add any other conditions in script or is there any other way to achieve "List Cis" behavior?

[Pratiksha7]

Thank you Rich.

Following query does work as you mentioned:
curl -H "Accept:application/json" --user "userName:password" "https://devXXXXX.service-now.com/api/now/table/cmdb_ci?sysparm_query=sys_idINjavascript:saListCis('SYSID')" --request GET --header "Accept:appl;2"