A \(\Pi^{0}_{1}\) class \(P\) is thin if every \(\Pi^{0}_{1}\) subclass \(Q\) of \(P\) is the intersection of \(P\) with some clopen set. In 1993, Cenzer, Downey, Jockusch and Shore initiated the study of Turing degrees of members of thin \(\Pi^{0}_{1}\) classes, and proved that degrees containing no members of thin \(\Pi^{0}_{1}\) classes can be recursively enumerable, and can be minimal degree below {\bf 0}\('\). In this paper, we work on this topic in terms of genericity, and prove that all 2-generic degrees contain no members of thin \(\Pi^{0}_{1}\) classes. In contrast to this, we show that all 1-generic degrees below {\bf 0}\('\) contain members of thin \(\Pi^{0}_{1}\) classes.