Scaffold design is one of the three most essential parts of tissue engineering. Platelet-rich plasma (PRP) and platelet-rich fibrin (PRF) have been used in clinics and regenerative medicine for years. However, the temporal release of their growth factors limits their efficacy in tissue engineering. In the present study, we planned to synthesize nanofibrous scaffolds with the incorporation of PRP and PRF by electrospinning method to evaluate the effect of the release of PRP and PRF growth factors on osteogenic gene expression, calcification, proliferation, and cell adhesion of human bone marrow mesenchymal stem cell (h-BMSC) as they are part of scaffold structures. Therefore, we combined PRP/PRF, derived from the centrifugation of whole blood, with gelatin and Polycaprolactone (PCL) and produced nanofibrous electrospun PCL/Gel/PRP and PCL/Gel/PRF scaffolds. Three groups of scaffolds were fabricated, and h-BMSCs were seeded on them: (1) PCL/Gel; (2) PCL/Gel/PRP; (3) PCL/Gel/PRF. MTS assay was performed to assess cell proliferation and adhesion, and alizarin red staining confirmed the formation of bone minerals during the experiment. The result indicated that PCL/Gel did not have any better outcomes than the PRP and PRF group in any study variants after the first day of the experiment. PCL/gelatin/PRF was more successful regarding cell proliferation and adhesion. Although PCL/gelatin/PRP showed more promising results on the last day of the experiment in mineralization and osteogenic gene expression, except RUNX2, in which the difference with PCL/gelatin/PRF group was not significant.