There is a wide consensus that type Ia supernovae (SN Ia) originate from the thermonuclear explosion of CO white dwarfs (WD), with the lack of hydrogen in the observed spectra as a distinctive feature. Here, we present SN 2016jae, which was classified as a Type Ia SN from a spectrum obtained soon after the discovery. The SN reached a B-band peak of -17.93 +- 0.34 mag, followed by a fast luminosity decline with sBV 0.56 +- 0.06 and inferred Dm15(B) of 1.88 +- 0.10 mag. Overall, the SN appears as a transitional event between normal SNe Ia and very dim SNe Ia such as 91bg-like SNe. Its peculiarity is that two late-time spectra taken at +84 and +142 days after the peak show a narrow line of Halpha (with full width at half-maximum of ~650 and 1000 kms-1, respectively). This is the third low-luminosity and fast-declining Type Ia SN after SN 2018cqj/ATLAS18qtd and SN 2018fhw/ASASSN-18tb, found in the 100IAS survey that shows resolved narrow Halpha line in emission in their nebular-phase spectra. We argue that the nebular Halpha emission originates in an expanding hydrogen-rich shell (with velocity < 1000 kms-1). The hydrogen shell velocity is too high to be produced during a common envelope phase, while it may be consistent with some material stripped from an H-rich companion star in a single-degenerate progenitor system. However, the derived mass of this stripped hydrogen is ~0.002-0.003 Msun, which is much less than that expected (>0.1 Msun) for standard models for these scenarios. Another plausible sequence of events is a weak SN ejecta interaction with a H-shell ejected by optically thick winds or a nova-like eruption on the C/O WD progenitor some years before the supernova explosion.
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