Abstract
In this paper we introduce the new class of QTAG-modules namely $\omega_1$-$(\omega+n)$-projective modules, which is an amalgamation of three important classes of modules: $n$-bounded modules, the direct sum of uniserial modules and the countably generated modules. This class is given many equivalent characterizations including being the smallest class containing the $(\omega+n)$-projective modules that is closed with respect to $\omega_1$-bijective homomorphisms.