Is it MWA JEN or MWAD JEN? Where does the second one come from if it's grammatically correct?

They say both in Creole.
Some people say Nan mwa jen m'a vin wè w.  In the month of June I will come to see you.
And some people say Nan mwad jen m'a vin wè w.  In the month of June I will come to see you.

mwad jen (from French mois de Juin)

Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words