Phabricator has a way to add Custom Fields¹ to various objects. It also allows configuring new object (Project, Task) subtypes² to show only specific custom fields.

It turns out, that documentation is not very clear³ on this and if there is a field mycompany:field and it must not be shown on a subtype then on subtype fields key it should be named "custom.mycmpany:field": { "disabled": true }, and not "mycompany:field": {"disabled": true}.

Alternatively, you can convert builtin form editable and hide that field. It is a low risk operation, but it still may prevent future builtin form fixes from propagating properly.³.