I'm a barber I work in this guy shop and he had me to sign a contract saying if I get fired or quit I can't open my own shop nor work 20 miles from sh

Although the law may be different in NC than in the states where I practice, there is generally no need for a contract to be notarized pr evem wrottem (with certain exceptions), but covenants not to compete are looked at with some disfavor, although not per se unenforceable.  They must be reasonable in both geogrpahic area and time.  While what is reasonable depends on the particular factgs of each case, my gut is that 20 miles would be considered too broad.  Also, you don't say how long the restriction runs; if in fact it is unlimited, that would likely be considered too long.  I assume the covenant only covers your work as a barber, not any type of work, as your question suggests; if it does, in fact, cover any work, it would not be enforced.  However, while the Court may hold tte entire covenant to be unenforceable, it may also "blue pencil" the provision, i.e. cut it back to what it considers reasonable, for example 1 mile and 1 year.