I’m working on my app for Barnard College and trying to figure out what to select for my “Field of Study Interest.” I’m hoping to major at Columbia in Linguistics (it isn’t offered at Barnard), so what should I select? Undecided? Thanks! 
It isn’t offered at Columbia either. Or more accurately, linguistics needs to combined with another major.
Barnard students cannot major in disciplines that are only offered at Columbia. They can of course take the classes, but they are not allowed to declare the major.
From the Barnard website:
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https://admissions.barnard.edu/academic-programs/majors-and-academic-programs
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“Design your own major … in cooperation with Columbia University” means that there’s a way for you to access most of what Columbia offers.
However, neither Barnard nor Columbia has had a freestanding linguistics department in decades. Barnard students can and do pursue studies of linguistics, but it is an interdisciplinary major – so not something you can select on the Common App.
You might think about what your focus might be and then select whatever major is closest. For example - a foreign language or literature major. You might get some ideas by browsing the list of affiliated faculty for linguistics at Columbia: http://bulletin.columbia.edu/columbia-college/departments-instruction/linguistics/#facultytext
Alternatively, of course, you can also opt for undecided. In most cases, the major indicated on your application won’t affect your chances for admission.