Certain types of oil, such as avocado or olive, can break a fast. At the same time, there are other kinds of oil individuals can consume during their fast without having a significant issue. Algae and fish oil are unlikely to break a fast as long as individuals consume them in normal doses. Normal doses of these supplements have only a few calories and don't include any digestible carbs. Branched-chain amino acids, otherwise known as BCAAs, should be avoided in oil or other forms while fasting because they cause an insulin response that keeps individuals from losing weight effectively. Expert opinions are divided on some other types of oil and whether they break a fast. For example, MCT oil technically breaks a fast since it's not black coffee, tea, or water. But clinically speaking, it shouldn't have a great enough impact on the metabolism to stop weight loss.
Get more information on what breaks a fast now.