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Electron ( z )‐nuclear ( R ) dynamics in the molecular high‐order harmonic generation (MHHG) from H 2 + driven by the plasmonic nonhomogeneous field, generated by the surface plasmon polaritons in the bowtie‐shaped nanostructure, have been theoretically investigated through solving the two dimensional time‐dependent Schrödinger equation with the Non‐Bohn‐Oppenheimer approximation. It is found that (i) due to the plasmonic enhancement of the laser intensity, the harmonic cutoff can be extended when the spatial position of H 2 + is away from the gap center of the nanostructure. However, due to the limit of the gap size, the threshold value of the harmonic cutoff can be obtained at a given position of H 2 + . (ii) Due to the asymmetric enhancement of the laser intensity in space, the extended higher harmonics are respectively from E ( t ) > 0 a.u. or E ( t ) < 0 a.u. for the cases of the positive and the negative spatial position of H 2 + . As a result, the intensities of the extended higher harmonics are different and can be controlled by changing the carrier‐envelope phase and the pulse duration of the laser field. (iii) In the few‐cycle pulse duration, the MHHG mainly comes from the multi‐photon resonance ionization (MPRI), while as the pulse duration increases, the MPRI, the charge‐resonance enhanced ionization (CREI) and even the dissociative ionization (DI) are contributed to the MHHG. Moreover, as the spatial position of H 2 + moves, the contributions of the MHHG from the MPRI, the CERI and the DI can be controlled. (iv) The contributions of the MHHG from the two‐H nuclei have been investigated and found that when E ( t ) > 0 a.u., the intensities of the harmonics from the negative‐H is higher than those from the positive‐H; while when E ( t ) < 0 a.u., the intensities of the harmonics from the positive‐H plays the main role in the MHHG. Moreover, the multi‐minima, caused by the two‐center interference can also be found. (v) Finally, by superposing a properly selected harmonics, a single isolated attosecond pulse (SIAP) with the full width at half maximum (FWHM) of 34 as can be obtained.