  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.
