In our cloud based contact center solution , we are using DMCC API "makeCall" for making outbound calls to external number in E.164 e.g. +14089999999 . However when we use getThirdPartyDeviceID API and set the request.setExtension to above number E.164 format we get an exception below

stationExtension = "+14089999999"

GetThirdPartyDeviceId request = new GetThirdPartyDeviceId();
request.setSwitchName(switchName);
request.setExtension(stationExtension);
request.setDeviceInstance(DeviceInstance.VALUE_0);

GetThirdPartyDeviceIdResponse response = dvSvc.getThirdPartyDeviceID(request);

12-22 23:06:07.724 INFO [473] usr=XXX- CSTA_Args: <?xml version="1.0" encoding="UTF-8"?>
<GetThirdPartyDeviceId xmlns="http://www.avaya.com/csta"><switchName>SW1</switchName><extension>+14089999999</extension><deviceInstance>0</deviceInstance></GetThirdPartyDeviceId>
12-22 23:06:07.961 INFO [473] usr=XXX- CSTA_Error_Code: <?xml version="1.0" encoding="UTF-8"?>
<CSTAErrorCode xmlns="http://www.ecma-international.org/standards/ecma-323/csta/ed3"><operation>invalidParameterValue</operation></CSTAErrorCode>

Does DMCC API support E.164 format ? Is there any other API to generate the Third Party Device ID using E.164 format?

What happens if you leave off the "+"?
Normally from my experience configuration on CM adds the + when needed if the call is routing out over a SIP trunk. Otherwise, I have not seen the "+" present in the signaling.

Without the + sign it works fine. We want to support E.164 format in our dialing from our application which requires a
"+" sign. Is there a version of DMCC API which has started supporting E.164 format with + sign ?

I have never had cause to investigate the functionality of the 'dialplan' in AE Services.

It does list "AE Services with DMCC clients using E.164ConversionServices" as one of the reasons that it is necessary.

https://www.devconnectprogram.com/fileMedia/download/56756fcb-2c7a-40f3-8d0e-5774512a3984 see the information beginning on page 288. See also the example on page 291.