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Can you help me, how to find the class on the AX & where should I write a code to deliver a new field on the sharepoint site(Online store). Can you help me by pointing the CLASS.
I will not, most likely, be able to tell you the *class name* because, based on your specific requirements the could be several of different places you need to modify but I can try help you with set of steps to achieve your goal:
You are probably aware that ecommerce is shipped with the SDK, which means you have source codes for the Publishing Portal site, so, you can look into the browser for the page name you want to modify and then you can find an appropriate page in the sources and debug it to have idea what entities should be modified for your specific task.
Without knowing what exactly you want to do with that field it is difficult to recommend something specific but, in general, if you want to send that new field all the way into AX then you might need to modify ecommerce UI side, CRT SDK/CRT DB/AX DB if the field you are looking for is not there.