I am synthesizing carbon nitride. There is someone who has synthesized the nitrogen rich carbon nitride, however, no one claimed to have synthesized nitrogen doped carbon nitride.
"Doping" always means very low content, generally less than a few %, and sometimes at the level of a few ppm. Nitrogen-doped carbon makes sense, but not nitrogen-doped carbon nitride, indeed, which is alwready a phase rich in N (by definition).
Doping is a technical word used for additive incorporation up to a concentration till band gap of the parent material does not change. It may be ppm level or so. However, when band gap changes on incorporation of additive element , one does not call doped material as a new alloy or compound is formed at higher concentration of additive element. Nitrogen rich carbon nitride can, therefore, not be called doped carbon.
First of all carbon nitride is the compound of carbon and nitrogen itself. It can be beta or graphitic C3N4. So here claiming N-doped carbon nitride is meaningless. But it is possible to get higher proportion of N in the compound. So the compound will be N-rich.