'in this morning' or 'this moring'

[Anonymous]

a. I woke up early in this morning.
b. I woke up early this morning.

I thought both is ok, but some say 'this' is adverb, so it shoud be 'b'.
Is this right?

Always appreciate your help.

 

[Francois]

a) is wrong (or at least uncommon)
b) is right and natural

FRC