Right of Abode/British passport

Do anyone know if a child of 6 years born to a British mother while in Nigeria can apply for right of abode from Nigeria to come and join her mother who is now resident in the UK. The mother was born in the UK and holds a british passport.
I want to also know if the child qualifies for British passport (from Nigeria) because both parents do not have officially recognised marriage at the time of the child birth in Nigeria. Although both parents are now in the UK and are now officially married, with the father currently holding a Residence Permit status (i.e  leave to remain in UK). The DNA report conducted in UK between the child and both parents (which was arranged through the British High Commission for child sampling in Nigeria) also support the paternity/maternity claim.

Please your urgent response is needed.

Ola.