That is, by the original publication that the manga appeared in in Japan, not the publisher of that magazine. It seems clear that I can search by publisher.

And if there's no direct search by publication, how do I find the publisher from the name of the magazine? The magazine I'd like to start with is Fellows.

Sorry if I'm being dense here.

I'm not completely sure I got your request right, but you could go on the page of a manga published on Fellows, like Sakamoto Desu ga? and then click on the "serialized in" link, in order to see a list of manga published on Fellows. If you instead mean that you want to make a research of a specific type of manga, and restrain the search to a single magazine, I don't believe it's possible.

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My current top 3:
Fullmetal Alchemist
Pandora Hearts
3-gatsu no Lion