In American universities, do teaching assistants and adjuncts get paid for holding office hours?
Your university should have a written policy, something like this. They may also have a published TA pay scale, something like this. Hopefully these kinds of resources can provide an answer to your question, however it is not uncommon that such positions (and their responsibilities/pay) are worked out between the TA and the course master on a per-course basis. If this is the case then you'll need to talk to the person who hired you.

My experience is that TA positions are usually a salaried position, and that specific course responsibilities are worked out between the TA and the course master. In a salaried position you don't get paid by how many hours you work. Office hours are considered a normal of part a TA's responsibilities, and if you're salaried then you don't get paid per hour. (This is a good thing- if I got paid only when students showed up I'd earn no money for two weeks and then work 24 hours straight before deadlines.)

The term "contact hours" will have a specific definition at your university, but where I've seen it used before it only applies to teaching in a scheduled group setting, not for office hours. Doing a scheduled recitation section for six students counts as a contact hour, but having a busy afternoon in office hours with six students in your office does not. For me, contact hours are scheduled lectures and recitations, not office hours.

If you feel like you are overworked or underpaid, there are a few suggestions:


Set an office hours schedule and don't feel bad about enforcing it. Most universities, if they have a policy, expect around 4-6 hours of office hours per week. Schedule them, make them known to students, and then don't feel bad about kicking people out when they're over.
If you feel like TA'ing is taking up too much of your time, go talk to the course master. If you have documented that there are too many students for you to handle individually, it is often possible to get funding approved for another TA.
If you feel like you're not being paid enough for your time, you're probably right. Welcome to the club... you'll graduate someday.