We study single-photon ionization of aligned ${\mathrm{H}}_2^{+}$ in low-intensity near-circular laser fields with lower photon energy numerically and analytically. The photoelectron momentum distribution (PMD) within the laser polarization plane, obtained by numerical simulations, shows a remarkable offset angle, which changes with changing the internuclear distance and the laser frequency. This phenomenon is different from that observed in recent experiments [Science 370, 339 (2020)], which is related to the PMD along the propagation direction of the laser. This phenomenon holds even for ${\mathrm{H}}_2^{+}$ with short-range Coulomb potentials but disappears for atoms, different from that observed in attoclock experiments. We show that the molecular Coulomb potential near the two atomic centers plays an important role here, and theoretical models associated with a more accurate continuum wave function of the molecule are needed for reproducing this phenomenon. This phenomenon also appears for other molecules such as ${\mathrm{N}}_2$. It can be useful for ultrafast probing of molecules with a high resolution of several attoseconds or even zeptoseconds.

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• Atomic & molecular processes in external fields
• Multiphoton or tunneling ionization & excitation
• Single- and few-photon ionization & excitation