The Shadow Kin were a race of fire-type humanoids that could only survive physically with the presence of a shadow. They were led by the Shadow King, Corakinus.
Corakinus described his kind as "an accident", saying they should never have been born into a universe of light. They lived in the Underneath. (TV: Co-Owner of a Lonely Heart)
Biology
The Shadow Kin could exist as "pure shadow", living unnoticed and untouchable in other people's shadows. In that form, they could only be killed if the person casting this shadow was killed as well. They could take on a solid form as well to kill their victims by surprise. Even in their most solid form, they could not exist when there were no shadows. (TV: For Tonight We Might Die)
Shadow Kin were capable of producing scimitars as weapons from their own bodies. (TV: For Tonight We Might Die, Co-Owner of a Lonely Heart)
History
The Shadow Kin emerged on the planet Rhodia amidst a war between the Rhodians and the Quill. Taking the native population of three billion off guard, the Shadow Kin drove them to near extinction with the exception of the Rhodian prince Charlie and a single Quill forced to serve as his protector as a punishment, who were relocated to Earth by the Twelfth Doctor.
Tracking the fugitives to Coal Hill Academy, the Shadow Kin, led by Corakinus, emerged through a tear in space-time at the school's prom night where they proceeded to mercilessly hunt for the pair before they were ultimately confronted by the Doctor, who Miss Quill had summoned for help. When the Doctor used the Shadow Kin's aversion to light against them, Corakinus and his kind were forced back through the tear from where they came which the Doctor subsequently sealed, though not entirely. Corakinus warned, however, that the Shadow Kin would return. (TV: For Tonight We Might Die)