In this paper, a method to discriminate between two target RNA sequences that differ by one nucleotide only is presented. The method relies on the formation of alternative structures, i.e., quadruplex–duplex hybrid (QDH) and duplex with dangling ends (Dss), after hybridization of DNA or RNA G-rich oligonucleotides with target sequences containing 5′–GGGCUGG–3′ or 5′–GGGCGGG–3′ fragments. Using biophysical methods, we studied the effect of oligonucleotide types (DNA, RNA), non-nucleotide modifications (aliphatic linkers or abasic), and covalently attached G4 ligand on the ability of G-rich oligonucleotides to assemble a G-quadruplex motif. We demonstrated that all examined non-nucleotide modifications could mimic the external loops in the G-quadruplex domain of QDH structures without affecting their stability. Additionally, some modifications, in particular the presence of two abasic residues in the G-rich oligonucleotide, can induce the formation of non-canonical QDH instead of the Dss structure upon hybridization to a target sequence containing the GGGCUGG motif. Our results offer new insight into the sequential requirements for the formation of G-quadruplexes and provide important data on the effects of non-nucleotide modifications on G-quadruplex formation.