  General relativistic instability supernovae at ~10 < z < ~15 are predicted to
be observed as red faint point sources, and they can be detected only in the
reddest filters in JWST/NIRCam (F444W and F356W). They should be observed as
persistent point sources with little flux variations for a couple of decades
because of time dilation. We search for static point sources detected only in
the F444W filter or only in the F444W and F356W filters in the early JWST deep
field data. No real point source of such kind is identified. Therefore, the
general relativistic instability supernova rate at ~10 < z < ~15 is constrained
to be less than ~ 8e-7 Mpc-3 yr-1 for the first time.
