This paper presents a computational and theoretical study of the yields for the C12 (p,γ) N13 and C12 (d,n) N13 nucleosynthesis reactions driven by high-energy (MeV) Coulomb explosion (CE) of (CH4) n and (CD4) n nanodroplets (n= 104 - 107, radii R0 =100-500 Å) in ultraintense near-infrared Gaussian laser fields (peak intensities IM = 1018 - 1019 W cm-2, pulse length τ=25 fs). Efficient nucleosynthesis with C12 nuclei requires the production of protons and deuterons in the energy range of 0.5-2.0 MeV, which is accomplished by CE of nanodroplets. The energy distributions of the nuclei were obtained from scaled molecular dynamics simulations and were utilized to calculate the energy averaged cross sections and the reaction yields for nucleosynthesis. Two distinct reaction modes were established pertaining to reactions inside the plasma filament volume (IF), and to reactions outside the plasma filament volume (OF). The dominating contribution to the total yields originates from the OF mode. The time resolved γ -ray emission for C12 (p,γ) N13 will be exhibited in distinct time intervals of 2-100 ps for the OF mode and of 65 fs-3 ps for the IF mode. Estimates of the yields were provided by incorporating the effects of nanodroplet size distributions that result in a slow size dependence of the yields in the range R0 >250 Å, and the effects of laser intensity attenuation in an assembly of nanodroplets that result in the decrease of the OF and IF yields due to the decrease of the effective plasma filament volume. For 400 Å nanodroplets at IM =4× 1018 - 1019 W cm-2, under realistic experimental conditions, the C12 (p,γ) N13 nucleosynthesis driven by CE of (CH4) n nanodroplets is characterized by a yield (per laser pulse) of ∼100, while the yield for the C12 (d,n) N13 nucleosynthesis driven by CE of (CD4) n clusters is ∼9× 104. Table-top nucleosynthesis driven by nanodroplet CE is amenable to experimental observation.