Does it possible to add a document type field in the online form of a custom record? For some reason, I'm not able to do so.

I don't believe you can do this. I think NetSuite limits this for security reasons. Not sure you would want a public form with the ability to upload files into your environment

I've done it with online custom case forms. Which are published externally.

I have managed also to do it with an online case form. Unfortunately, is not possible by online form from a custom record.

Found an old case I created, NS Support said it wasn't possible with Custom Record types.. This was a few years ago though.

I will try to hack it with HTML netsuite