For a « realistic » way to have telepathy, here what I know and think so far :
1. I know that technologies using brainwaves as interface already exist in some form. Many animals have electroreception through the organs called ampullae of Lorenzini. How could a mutant version transmit and not just receive electromagnetic waves.
2. I am aware that the side-effects of constant exposition to low level and non-ionising electromagnetic radiations(radiowaves) includes : nausea, headaches, fatigue, suicidal thoughts leading to suicide, depression, loss of libido, electromagnetic hypersensitivity, cataract formations.
3. The way the brain translate this form of stimuli into comprehensive information is the last thing to explain that elude me.
But beside that last point, in what ways could the facts I presented be portrayed in a story ?