What could cause a sharp, burning and tingling pain in the outside and just below my right patella that is felt only when kneeling?

Patella tendonitis? This can be from inflammation of the patella tendon, it can be from arthritis under the knee cap, it can be from a skin neuroma in that area but all things can be improved if you get examined and the correct diagnosis. An orthopaedic surgeon would be an appropriate person to help you. Good luck.
Tendinopathy? In this area you could have arthritis beneath the patellar, inflammed synovium about the knee cap, or the most likely....Tendinopathy ot the patellar tendon. Knee pads can help when kneeling. Hamstring stretching may help chronic pain. If things persist, have it checked.