See below. One particle, a photon, already exists and fits the properties listed, but it would be difficult to prove the existence of another.
Work Step by Step
Being massless and electrically neutral, a “neutrinolet” would not interact via the gravitational or electromagnetic forces. If it had no color charge, then it would not interact via the strong force. If were specified that it didn’t feel the weak force either, basically, it would have no interactions with matter. It would be very difficult to prove that it exists.