Despite the successes of antibodies as therapeutic binding proteins, they still face production and design challenges. Alternative binding scaffolds of smaller size have been developed to overcome these issues. A subset of these alternative scaffolds recognizes target molecules through mutations to a set of surface resides, which does not alter their backbone structures. While the computational design of antibodies for target epitopes has been explored in depth, the same has not been done for alternative scaffolds. The commonly used dock-and-mutate approach for binding proteins, including antibodies, is limited because it uses a constant sequence and structure representation of the scaffold. Docking fixed-backbone scaffolds with a varied group of surface amino acids increases the chances of identifying superior starting poses that can be improved with subsequent mutations. In this work, we have developed MutDock, a novel computational approach that simultaneously docks and mutates fixed backbone scaffolds for binding a target epitope by identifying a minimum number of hydrogen bonds. The approach is broadly divided into two steps. The first step uses pairwise distance alignment of hydrogen bond-forming areas of scaffold residues and compatible epitope atoms. This step considers both native and mutated rotamers of scaffold residues. The second step mutates clashing variable interface residues and thermodynamically unfavorable residues to create additional strong interactions. MutDock was used to dock two scaffolds, namely, Affibodies and DARPins, with ten randomly selected antigens. The energies of the docked poses were minimized and binding energies were compared with docked poses from ZDOCK and HADDOCK. The top MutDock poses consisted of higher and comparable binding energies than the top ZDOCK and HADDOCK poses, respectively. This work contributes to the discovery of novel binders based on smaller-sized, fixed-backbone protein scaffolds.