In this case there is no paradox.
yeah, there's a popular story behind it. You presented it in short thus losing its point

But then while looking for it I see that many people online degraded that thing to 2 sentences
Full version:
Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves, some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves.
Under this scenario, we can ask the following question: Does the barber shave himself?
The answer is obviously a contradiction.
In logic 'x and not x'