Modification of DNA aptamers is aimed at increasing their thermodynamic stability, and improving affinity and resistance to biodegradation. G-quadruplex DNA aptamers are a family of affinity ligands that form non-canonical DNA assemblies based on a G-tetrads stack. Modification of the quadruplex core is challenging since it can cause complete loss of affinity of the aptamer. On the other hand, increased thermodynamic stability could be a worthy reward. In the current paper, we developed new three- and four-layer modified analogues of the thrombin binding aptamer with high thermal stability, which retain anticoagulant activity against alpha-thrombin. In the modified aptamers, one or two G-tetrads contained non-natural anti-preferred alpha-deoxyguanosines at specific positions. The use of this nucleotide analogue made it possible to control the topology of the modified structures. Due to the presence of non-natural tetrads, we observed some decrease in the anticoagulant activity of the modified aptamers compared to the natural prototype. This negative effect was completely compensated by conjugation of the aptamers with optimized tripeptide sequences.