Maithils are East Indian not North Indian
I hail from Bhagalpur (historic capital of ancient AngDesh kingdom with Angika dialect of Maithili as lingua franca), have travelled across East India (Assom, Bihar, Bengal, Jharkhand and Odisha) with decent understanding of languages spoken in all these states and hence feel eligible to answer this. Geoculturally, both Bihar and Jharkhand are closer to Bengal, Odisha (part of erstwhile British Bengal Presidency) and hence rightly called as 'East Indian'. Yet some residents of these two states may wish to call themselves as North Indian, mostly because of them associating with 'Hindi' identity. Now coming to details around Bihar (those who wish to study linguistic geography of Bihar are welcome to refer 8-volume series Seven Grammars of Bihar by linguist George Grierson) : Bihar has a highly heterogeneous populace due to it being divided into three major linguistically diverse segments (with ballpark figure) : Maithili Family ≈ {Bajjika 12%} + {Kendriya Maithili 12%} ...