In the morning vs on the morning?

These are four quotes from The Guardian:

If you have trouble waking up in the mornings, having some light coming in through the windows may help. 

Early in the morning of 26 September, alarms went off and computers sent signals that a US Minuteman intercontinental ballistic missile had ...

The simple story would be this: on the morning of 12 August 2012, a 16-year-old girl woke up in an unfamiliar basement in Steubenville, a football-obsessed town on the border of West Virginia.

One hundred years ago this Sunday, at 11 o’clock on the morning of 11 November 1918, the guns fell silent in France.

So, what is the correct option: in the morning or on the morning?

Before we go crazy, let’s go to Cambridge Dictionary:

So, in the morning, in the afternoon, in the evening and at the night, but if we speak about some specific morning, afternoon, evening or night we'll use on the morning of.., on the afternoon, on the evening, in the night:

What happened on the afternoon of 14th July in 1789?

What happened in the night of Varennes?