The detection of trace protein biomarkers is essential in the diagnostic field. Protein detection systems ranging from widely used enzyme-linked immunosorbent assays to simple, inexpensive approaches, such as lateral flow immunoassays, play critical roles in medical and drug research. Despite continuous progress, current systems are insufficient for the diagnosis of diseases that require high sensitivity. In this study, we developed a heterogeneous sandwich-type sensing platform based on recombinase polymerase amplification using DNA aptamers specific to the target biomarker. Only the DNA bound to the target in the form of a heterogeneous sandwich was selectively amplified, and the fluorescence signal of an intercalating dye added before the amplification reaction was detected, thereby enabling high specificity and sensitivity. We applied this method for the detection of protein biomarkers for various infectious diseases including severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and observed attomolar-level detection of biomarkers and low cross-reactivity between different viruses. We also confirmed detection efficiency of the proposed method using clinical samples. These results demonstrate that the proposed sensing platform can be used to diagnose various diseases requiring high sensitivity, specificity, and accuracy.