This work presents a study on laser wakefield electron acceleration in the self-modulated regime (SM-LWFA) using 50-fs laser pulses with energy on the mJ scale, at λ = 0.8 μm, impinging on a thin H 2 gas jet. Particle-in-cell simulations were performed using laser peak powers ranging from sub-terawatt to a few terawatts and plasma densities varying from the relativistic self-focusing threshold up to values close to the critical density. The differences in the obtained acceleration processes are discussed. Results show that bunched electron beams with full charge on the nC scale and kinetic energy in the MeV range can be produced and configurations with peak density in the range 0.5-5 × 10 20 atoms/cm 3 generate electrons with maximum energies. In this range, some simulations generated quasimonoenergetic bunches with ∼0.5% of the total accelerated charge and we show that the beam characteristics, process dynamics, and operational parameters are close to those expected for the blowout regime. The configurations that led to quasimonoenergetic bunches from the sub-TW SM-LWFA regime allow the use of laser systems with repetition rates in the kHz range, which can be beneficial for practical applications.