Ok, let see these sentences:
"He fed his dog in the morning"
"He fed his dog this morning"
"He fed his dog in this morning"
So, which sentence is correct?
It seems that the 2nd one is used more commonly
As a native speaker, I can say that only 1 and 2 are correct in the UK and USA. From a cursory search I see that it is possible that some African or Asian varieties of English might use 3. I'm not an expert on those.
'He always fed his dog in the morning'.
'On the day of the murder, he fed his dog in the morning.'
Notes
Google ngram: this morning,in the morning,in this morning
Although the words 'in this morning' do occur, if you read the resulting texts, you'll see that they are mostly used in a different sense, e.g. 'I could have slept in this morning' where the verb is 'to sleep in'.
Thus we have the strange discrepancies in the contrasts shown in Exx. 16, showing separate effects of the, this and that. (16) a. this morning, *on this morning, *in this morning b. *the morning, *on the morning, in the morning c. that morning,
Complex Sentences in Grammar and Discourse Essays in honor of Sandra A. Thompson
Edited by Joan L. Bybee and Michael Noonan University of New Mexico / University of Wisconsin at Milwaukee