Shopify API custom fulfillment

I sell digital service (no actual tracking number needed) and I'm using a custom script that needs to fulfill orders (mark as fulfilled) via POST API call. The error I get is

"The fulfillment order's assigned fulfillment service must be of api type" 

 I have all read and write settings for the API settings. I have looked for this question on the community and the relevant answers did not resolve my issues (creating custom fulfillment service from shipping settings, read&write access, tried to install a self-created developer app, but the link was broken).

I think if I can get my app installed on my store I might be able to set the fulfillment service to api type, but I can't even get it installed. All I want to do is to be able to mark my order as fulfilled via an API call. Any help is greatly appreciated.