Accessory branch of inferior alveolar nerve: clinical significance?

Yes, this branch have clinical significance during implant placement due to low space.

Artery branch not a mental nerve branch.

That is not a branch of the alveolar nerve. The crown to root ration that was ingrained to us in dental school has lost its validity when it comes to dental Implants. Bicon and Quantum implants have thousands of successful cases with short implants. Clinically instead of bone loss we are observing bone growth. When I first started placing implants I always chose the longest size available. Right now I am convince that all that is needed is a 6mm implant. Of course I am sure that many will not agree, and that is fine, I am offering my clinical experience.

My comment is that this may or may not be a blood vessel but the bleeding can be stopped intra- operatively. My issue is that Your planned implant should be 1.5 mm from bicuspid to avoid a mesial cantilever. I would also suggest two implants splinted to decrease force factors on a terminal implant especially with short implant height. You can’t splint Bicons.

We need a coronal image to determine if this is important.

Cases like this are TROUBLE. Do yourself a favor either do a vertical ridge augmentation and fix the defect or tell the patient to do a partial denture. We don't need to take risks like this. It's ok to say no.

Could experts in the field of implantology provide some insights as to whether it is permissible to sacrifice these small neurovascular bundles that arise form inferior alveolar nerve all the way to the crest of the ridge, as seen in type 3 or 4 inferior alveolar nerve types.