Which area of psychology studies false beliefs? Imagine a person has some false beliefs, which are also reflected then in his actions:

I  don't want to interact with people because I don't trust them and 90% of time they will betray me
If I form close relationship with people then I will not be able to move to different country because I will miss them
....

We can bring similar beliefs. I am interested which direction in psychology studies this situation when person has such beliefs? And tries to correct them
These are typically called cognitive distortions and are a mainstay of CBT, but are equally likely to be addressed by any cognitive psychotherapist.  This is usually done by building skills to identify and challenge such thoughts.
In the much older (and largely outdated) school of psychoanalysis, these are typically referred to as a defense mechanism called rationalizations.
In contrast, behavioral therapies are less likely to directly address such thoughts.  With this paradigm, distortions typically subside once the underlying behavior pattern is addressed (eg, by improving social skills, and actually making friends).