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Level-restricted paths play an important role in crystal theory. Theycorrespond to certain highest weight vectors of modules of quantum affinealgebras. We show that the recently established bijection betweenLittlewood--Richardson tableaux and rigged configurations is well-behaved withrespect to level-restriction and give an explicit characterization oflevel-restricted rigged configurations. As a consequence a new generalfermionic formula for the level-restricted generalized Kostka polynomial isobtained. Some coset branching functions of type $A$ are computed by takinglimits of these fermionic formulas.Comment: 67 pages, axodraw style file neede

Fermionic Formulas for Level-Restricted Generalized Kostka Polynomials and Coset Branching Functions