Entanglement-assisted quantum error correcting codes (EAQECCs) play a significant role in protecting information from decoherence and noise. In this work, we construct six families of new EAQECCs lengths $$n=(q^2+1)/a$$ , $$n=q^2+1$$ $$n=(q^2+1)/2$$ cyclic codes, where $$a=m^2+1$$ ( $$m\ge 1$$ is odd) q an odd prime power with the form $$a|(q+m)$$ or $$a|(q-m)$$ . Moreover, those are entangleme...